data.complex.exponential_bounds
⟷
Mathlib.Data.Complex.ExponentialBounds
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -81,9 +81,9 @@ theorem log_two_near_10 : |log 2 - 287209 / 414355| ≤ 1 / 10 ^ 10 :=
assumption
have t : |(2⁻¹ : ℝ)| = 2⁻¹ := by rw [abs_of_pos]; norm_num
have z := Real.abs_log_sub_add_sum_range_le (show |(2⁻¹ : ℝ)| < 1 by rw [t]; norm_num) 34
- rw [t] at z
- norm_num1 at z
- rw [one_div (2 : ℝ), log_inv, ← sub_eq_add_neg, _root_.abs_sub_comm] at z
+ rw [t] at z
+ norm_num1 at z
+ rw [one_div (2 : ℝ), log_inv, ← sub_eq_add_neg, _root_.abs_sub_comm] at z
apply le_trans (_root_.abs_sub_le _ _ _) (add_le_add z _)
simp_rw [sum_range_succ]
norm_num
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -57,7 +57,7 @@ theorem exp_one_lt_d9 : exp 1 < 2.7182818286 :=
#print Real.exp_neg_one_gt_d9 /-
theorem exp_neg_one_gt_d9 : 0.36787944116 < exp (-1) :=
by
- rw [exp_neg, lt_inv _ (exp_pos _)]
+ rw [NormedSpace.exp_neg, lt_inv _ (exp_pos _)]
refine' lt_of_le_of_lt (sub_le_iff_le_add.1 (abs_sub_le_iff.1 exp_one_near_10).1) _
all_goals norm_num
#align real.exp_neg_one_gt_d9 Real.exp_neg_one_gt_d9
@@ -66,7 +66,7 @@ theorem exp_neg_one_gt_d9 : 0.36787944116 < exp (-1) :=
#print Real.exp_neg_one_lt_d9 /-
theorem exp_neg_one_lt_d9 : exp (-1) < 0.3678794412 :=
by
- rw [exp_neg, inv_lt (exp_pos _)]
+ rw [NormedSpace.exp_neg, inv_lt (exp_pos _)]
refine' lt_of_lt_of_le _ (sub_le_comm.1 (abs_sub_le_iff.1 exp_one_near_10).2)
all_goals norm_num
#align real.exp_neg_one_lt_d9 Real.exp_neg_one_lt_d9
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Joseph Myers
-/
-import Mathbin.Data.Complex.Exponential
-import Mathbin.Analysis.SpecialFunctions.Log.Deriv
+import Data.Complex.Exponential
+import Analysis.SpecialFunctions.Log.Deriv
#align_import data.complex.exponential_bounds from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Joseph Myers
-
-! This file was ported from Lean 3 source module data.complex.exponential_bounds
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Complex.Exponential
import Mathbin.Analysis.SpecialFunctions.Log.Deriv
+#align_import data.complex.exponential_bounds from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
/-!
# Bounds on specific values of the exponential
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -23,6 +23,7 @@ namespace Real
open IsAbsoluteValue Finset CauSeq Complex
+#print Real.exp_one_near_10 /-
theorem exp_one_near_10 : |exp 1 - 2244083 / 825552| ≤ 1 / 10 ^ 10 :=
by
apply exp_approx_start
@@ -31,7 +32,9 @@ theorem exp_one_near_10 : |exp 1 - 2244083 / 825552| ≤ 1 / 10 ^ 10 :=
refine' exp_approx_end' _ (by norm_num1 <;> rfl) _ (by norm_cast <;> rfl) (by simp) _
rw [_root_.abs_one, abs_of_pos] <;> norm_num1
#align real.exp_one_near_10 Real.exp_one_near_10
+-/
+#print Real.exp_one_near_20 /-
theorem exp_one_near_20 : |exp 1 - 363916618873 / 133877442384| ≤ 1 / 10 ^ 20 :=
by
apply exp_approx_start
@@ -40,29 +43,39 @@ theorem exp_one_near_20 : |exp 1 - 363916618873 / 133877442384| ≤ 1 / 10 ^ 20
refine' exp_approx_end' _ (by norm_num1 <;> rfl) _ (by norm_cast <;> rfl) (by simp) _
rw [_root_.abs_one, abs_of_pos] <;> norm_num1
#align real.exp_one_near_20 Real.exp_one_near_20
+-/
+#print Real.exp_one_gt_d9 /-
theorem exp_one_gt_d9 : 2.7182818283 < exp 1 :=
lt_of_lt_of_le (by norm_num) (sub_le_comm.1 (abs_sub_le_iff.1 exp_one_near_10).2)
#align real.exp_one_gt_d9 Real.exp_one_gt_d9
+-/
+#print Real.exp_one_lt_d9 /-
theorem exp_one_lt_d9 : exp 1 < 2.7182818286 :=
lt_of_le_of_lt (sub_le_iff_le_add.1 (abs_sub_le_iff.1 exp_one_near_10).1) (by norm_num)
#align real.exp_one_lt_d9 Real.exp_one_lt_d9
+-/
+#print Real.exp_neg_one_gt_d9 /-
theorem exp_neg_one_gt_d9 : 0.36787944116 < exp (-1) :=
by
rw [exp_neg, lt_inv _ (exp_pos _)]
refine' lt_of_le_of_lt (sub_le_iff_le_add.1 (abs_sub_le_iff.1 exp_one_near_10).1) _
all_goals norm_num
#align real.exp_neg_one_gt_d9 Real.exp_neg_one_gt_d9
+-/
+#print Real.exp_neg_one_lt_d9 /-
theorem exp_neg_one_lt_d9 : exp (-1) < 0.3678794412 :=
by
rw [exp_neg, inv_lt (exp_pos _)]
refine' lt_of_lt_of_le _ (sub_le_comm.1 (abs_sub_le_iff.1 exp_one_near_10).2)
all_goals norm_num
#align real.exp_neg_one_lt_d9 Real.exp_neg_one_lt_d9
+-/
+#print Real.log_two_near_10 /-
theorem log_two_near_10 : |log 2 - 287209 / 414355| ≤ 1 / 10 ^ 10 :=
by
suffices |log 2 - 287209 / 414355| ≤ 1 / 17179869184 + (1 / 10 ^ 10 - 1 / 2 ^ 34)
@@ -79,14 +92,19 @@ theorem log_two_near_10 : |log 2 - 287209 / 414355| ≤ 1 / 10 ^ 10 :=
norm_num
rw [abs_of_pos] <;> norm_num
#align real.log_two_near_10 Real.log_two_near_10
+-/
+#print Real.log_two_gt_d9 /-
theorem log_two_gt_d9 : 0.6931471803 < log 2 :=
lt_of_lt_of_le (by norm_num1) (sub_le_comm.1 (abs_sub_le_iff.1 log_two_near_10).2)
#align real.log_two_gt_d9 Real.log_two_gt_d9
+-/
+#print Real.log_two_lt_d9 /-
theorem log_two_lt_d9 : log 2 < 0.6931471808 :=
lt_of_le_of_lt (sub_le_iff_le_add.1 (abs_sub_le_iff.1 log_two_near_10).1) (by norm_num)
#align real.log_two_lt_d9 Real.log_two_lt_d9
+-/
end Real
mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Joseph Myers
! This file was ported from Lean 3 source module data.complex.exponential_bounds
-! leanprover-community/mathlib commit 402f8982dddc1864bd703da2d6e2ee304a866973
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.SpecialFunctions.Log.Deriv
/-!
# Bounds on specific values of the exponential
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -68,9 +68,9 @@ theorem log_two_near_10 : |log 2 - 287209 / 414355| ≤ 1 / 10 ^ 10 :=
assumption
have t : |(2⁻¹ : ℝ)| = 2⁻¹ := by rw [abs_of_pos]; norm_num
have z := Real.abs_log_sub_add_sum_range_le (show |(2⁻¹ : ℝ)| < 1 by rw [t]; norm_num) 34
- rw [t] at z
- norm_num1 at z
- rw [one_div (2 : ℝ), log_inv, ← sub_eq_add_neg, _root_.abs_sub_comm] at z
+ rw [t] at z
+ norm_num1 at z
+ rw [one_div (2 : ℝ), log_inv, ← sub_eq_add_neg, _root_.abs_sub_comm] at z
apply le_trans (_root_.abs_sub_le _ _ _) (add_le_add z _)
simp_rw [sum_range_succ]
norm_num
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -66,15 +66,8 @@ theorem log_two_near_10 : |log 2 - 287209 / 414355| ≤ 1 / 10 ^ 10 :=
by
norm_num1 at *
assumption
- have t : |(2⁻¹ : ℝ)| = 2⁻¹ := by
- rw [abs_of_pos]
- norm_num
- have z :=
- Real.abs_log_sub_add_sum_range_le
- (show |(2⁻¹ : ℝ)| < 1 by
- rw [t]
- norm_num)
- 34
+ have t : |(2⁻¹ : ℝ)| = 2⁻¹ := by rw [abs_of_pos]; norm_num
+ have z := Real.abs_log_sub_add_sum_range_le (show |(2⁻¹ : ℝ)| < 1 by rw [t]; norm_num) 34
rw [t] at z
norm_num1 at z
rw [one_div (2 : ℝ), log_inv, ← sub_eq_add_neg, _root_.abs_sub_comm] at z
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -43,14 +43,16 @@ theorem exp_one_lt_d9 : exp 1 < 2.7182818286 :=
theorem exp_neg_one_gt_d9 : 0.36787944116 < exp (-1) := by
rw [exp_neg, lt_inv _ (exp_pos _)]
- refine' lt_of_le_of_lt (sub_le_iff_le_add.1 (abs_sub_le_iff.1 exp_one_near_10).1) _
- all_goals norm_num
+ · refine' lt_of_le_of_lt (sub_le_iff_le_add.1 (abs_sub_le_iff.1 exp_one_near_10).1) _
+ norm_num
+ · norm_num
#align real.exp_neg_one_gt_d9 Real.exp_neg_one_gt_d9
theorem exp_neg_one_lt_d9 : exp (-1) < 0.3678794412 := by
rw [exp_neg, inv_lt (exp_pos _)]
- refine' lt_of_lt_of_le _ (sub_le_comm.1 (abs_sub_le_iff.1 exp_one_near_10).2)
- all_goals norm_num
+ · refine' lt_of_lt_of_le _ (sub_le_comm.1 (abs_sub_le_iff.1 exp_one_near_10).2)
+ norm_num
+ · norm_num
#align real.exp_neg_one_lt_d9 Real.exp_neg_one_lt_d9
set_option tactic.skipAssignedInstances false in
This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0
branch as we update to intermediate nightlies.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>
@@ -53,6 +53,7 @@ theorem exp_neg_one_lt_d9 : exp (-1) < 0.3678794412 := by
all_goals norm_num
#align real.exp_neg_one_lt_d9 Real.exp_neg_one_lt_d9
+set_option tactic.skipAssignedInstances false in
theorem log_two_near_10 : |log 2 - 287209 / 414355| ≤ 1 / 10 ^ 10 := by
suffices |log 2 - 287209 / 414355| ≤ 1 / 17179869184 + (1 / 10 ^ 10 - 1 / 2 ^ 34) by
norm_num1 at *
@@ -2,15 +2,12 @@
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Joseph Myers
-
-! This file was ported from Lean 3 source module data.complex.exponential_bounds
-! leanprover-community/mathlib commit 402f8982dddc1864bd703da2d6e2ee304a866973
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Complex.Exponential
import Mathlib.Analysis.SpecialFunctions.Log.Deriv
+#align_import data.complex.exponential_bounds from "leanprover-community/mathlib"@"402f8982dddc1864bd703da2d6e2ee304a866973"
+
/-!
# Bounds on specific values of the exponential
-/
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file