Changes since the initial port

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.

Changes in mathlib3

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

7e5137f5

bump to nightly-2024-04-19-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

a9e81450

Diff

@@ -57,9 +57,9 @@ theorem tendsto_sum_pi_div_four :
     convert
       (((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
             tendsto_inv_atTop_zero).comp
-        tendsto_nat_cast_atTop_atTop
+        tendsto_natCast_atTop_atTop
     · ext k
-      simp only [NNReal.coe_nat_cast, Function.comp_apply, NNReal.coe_rpow]
+      simp only [NNReal.coe_natCast, Function.comp_apply, NNReal.coe_rpow]
       rw [← rpow_mul (Nat.cast_nonneg k) (-1 / (2 * (k : ℝ) + 1)) (2 * (k : ℝ) + 1),
         @div_mul_cancel₀ _ _ (2 * (k : ℝ) + 1) _
           (by norm_cast; simp only [Nat.succ_ne_zero, not_false_iff]),

7e5137f5

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -61,7 +61,7 @@ theorem tendsto_sum_pi_div_four :
     · ext k
       simp only [NNReal.coe_nat_cast, Function.comp_apply, NNReal.coe_rpow]
       rw [← rpow_mul (Nat.cast_nonneg k) (-1 / (2 * (k : ℝ) + 1)) (2 * (k : ℝ) + 1),
-        @div_mul_cancel _ _ (2 * (k : ℝ) + 1) _
+        @div_mul_cancel₀ _ _ (2 * (k : ℝ) + 1) _
           (by norm_cast; simp only [Nat.succ_ne_zero, not_false_iff]),
         rpow_neg_one k, sub_eq_add_neg]
     · simp only [add_zero, add_right_neg]
@@ -105,7 +105,7 @@ theorem tendsto_sum_pi_div_four :
         ring
       · simp only [Nat.add_succ_sub_one, add_zero, mul_one, id.def, Nat.cast_bit0, Nat.cast_add,
           Nat.cast_one, Nat.cast_mul]
-        rw [← mul_assoc, @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; linarith),
+        rw [← mul_assoc, @div_mul_cancel₀ _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; linarith),
           pow_mul x 2 i, ← mul_pow (-1) (x ^ 2) i]
         ring_nf
     convert (has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
@@ -151,7 +151,7 @@ theorem tendsto_sum_pi_div_four :
     _ ≤ 1 * (1 - U) + U ^ (2 * k) * (U - 0) :=
       (le_trans (abs_add (f 1 - f U) (f U - f 0)) (add_le_add mvt1 mvt2))
     _ = 1 - U + U ^ (2 * k) * U := by ring
-    _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) := by rw [← pow_succ' (U : ℝ) (2 * k)]; norm_cast
+    _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) := by rw [← pow_succ (U : ℝ) (2 * k)]; norm_cast
 #align real.tendsto_sum_pi_div_four Real.tendsto_sum_pi_div_four
 -/

7e5137f5

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -132,15 +132,15 @@ theorem tendsto_sum_pi_div_four :
     by
     rintro x ⟨hx_left, hx_right⟩
     have hincr := pow_le_pow_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
-    rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr 
-    rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right 
+    rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr
+    rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_of_lt hx_right)))]
   have hbound2 : ∀ x ∈ Ico 0 (U : ℝ), |f' x| ≤ U ^ (2 * k) :=
     by
     rintro x ⟨hx_left, hx_right⟩
     have hincr := pow_le_pow_left hx_left (le_of_lt hx_right) (2 * k)
-    rw [← abs_of_nonneg hx_left] at hincr hx_right 
-    rw [← abs_of_nonneg hU2] at hU1 hx_right 
+    rw [← abs_of_nonneg hx_left] at hincr hx_right
+    rw [← abs_of_nonneg hU2] at hU1 hx_right
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_trans (le_of_lt hx_right) hU1)))]
   -- (6) We twice apply the Mean Value Theorem to obtain bounds on `f` from the bounds on `f'`
   have mvt1 := norm_image_sub_le_of_norm_deriv_le_segment' hderiv1 hbound1 _ (right_mem_Icc.mpr hU1)

7e5137f5

bump to nightly-2023-12-20-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

058cd493

Diff

@@ -131,14 +131,14 @@ theorem tendsto_sum_pi_div_four :
   have hbound1 : ∀ x ∈ Ico (U : ℝ) 1, |f' x| ≤ 1 :=
     by
     rintro x ⟨hx_left, hx_right⟩
-    have hincr := pow_le_pow_of_le_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
+    have hincr := pow_le_pow_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
     rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr 
     rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right 
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_of_lt hx_right)))]
   have hbound2 : ∀ x ∈ Ico 0 (U : ℝ), |f' x| ≤ U ^ (2 * k) :=
     by
     rintro x ⟨hx_left, hx_right⟩
-    have hincr := pow_le_pow_of_le_left hx_left (le_of_lt hx_right) (2 * k)
+    have hincr := pow_le_pow_left hx_left (le_of_lt hx_right) (2 * k)
     rw [← abs_of_nonneg hx_left] at hincr hx_right 
     rw [← abs_of_nonneg hU2] at hU1 hx_right 
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_trans (le_of_lt hx_right) hU1)))]

7e5137f5

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Benjamin Davidson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Benjamin Davidson
 -/
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
+import Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
 
 #align_import data.real.pi.leibniz from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"

7e5137f5

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -48,7 +48,7 @@ local notation "|" x "|" => abs x
 theorem tendsto_sum_pi_div_four :
     Tendsto (fun k => ∑ i in Finset.range k, (-(1 : ℝ)) ^ i / (2 * i + 1)) atTop (𝓝 (π / 4)) :=
   by
-  rw [tendsto_iff_norm_tendsto_zero, ← tendsto_zero_iff_norm_tendsto_zero]
+  rw [tendsto_iff_norm_sub_tendsto_zero, ← tendsto_zero_iff_norm_tendsto_zero]
   -- (1) We introduce a useful sequence `u` of values in [0,1], then prove that another sequence
   --     constructed from `u` tends to `0` at `+∞`
   let u := fun k : ℕ => (k : NNReal) ^ (-1 / (2 * (k : ℝ) + 1))

7e5137f5

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Benjamin Davidson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Benjamin Davidson
-
-! This file was ported from Lean 3 source module data.real.pi.leibniz
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
 
+#align_import data.real.pi.leibniz from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-! ### Leibniz's Series for Pi 
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

7e5137f5

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -22,9 +22,9 @@ open Filter Set
 
 open scoped Classical BigOperators Topology Real
 
--- mathport name: abs
 local notation "|" x "|" => abs x
 
+#print Real.tendsto_sum_pi_div_four /-
 /-- This theorem establishes **Leibniz's series for `π`**: The alternating sum of the reciprocals
   of the odd numbers is `π/4`. Note that this is a conditionally rather than absolutely convergent
   series. The main tool that this proof uses is the Mean Value Theorem (specifically avoiding the
@@ -156,6 +156,7 @@ theorem tendsto_sum_pi_div_four :
     _ = 1 - U + U ^ (2 * k) * U := by ring
     _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) := by rw [← pow_succ' (U : ℝ) (2 * k)]; norm_cast
 #align real.tendsto_sum_pi_div_four Real.tendsto_sum_pi_div_four
+-/
 
 end Real

7e5137f5

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -155,7 +155,6 @@ theorem tendsto_sum_pi_div_four :
       (le_trans (abs_add (f 1 - f U) (f U - f 0)) (add_le_add mvt1 mvt2))
     _ = 1 - U + U ^ (2 * k) * U := by ring
     _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) := by rw [← pow_succ' (U : ℝ) (2 * k)]; norm_cast
-    
 #align real.tendsto_sum_pi_div_four Real.tendsto_sum_pi_div_four
 
 end Real

7e5137f5

bump to nightly-2023-06-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

fe176e9b

Diff

@@ -4,13 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Benjamin Davidson
 
 ! This file was ported from Lean 3 source module data.real.pi.leibniz
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
 
-/-! ### Leibniz's Series for Pi -/
+/-! ### Leibniz's Series for Pi 
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.-/
 
 
 namespace Real

f2ce6086

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -54,7 +54,8 @@ theorem tendsto_sum_pi_div_four :
   let u := fun k : ℕ => (k : NNReal) ^ (-1 / (2 * (k : ℝ) + 1))
   have H : tendsto (fun k : ℕ => (1 : ℝ) - u k + u k ^ (2 * (k : ℝ) + 1)) at_top (𝓝 0) :=
     by
-    convert(((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
+    convert
+      (((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
             tendsto_inv_atTop_zero).comp
         tendsto_nat_cast_atTop_atTop
     · ext k
@@ -96,7 +97,8 @@ theorem tendsto_sum_pi_div_four :
     have has_deriv_at_b : ∀ i ∈ Finset.range k, HasDerivAt (b i) ((-x ^ 2) ^ i) x :=
       by
       intro i hi
-      convert HasDerivAt.const_mul ((-1 : ℝ) ^ i / (2 * i + 1))
+      convert
+        HasDerivAt.const_mul ((-1 : ℝ) ^ i / (2 * i + 1))
           (@HasDerivAt.pow _ _ _ _ _ (2 * i + 1) (hasDerivAt_id x))
       · ext y
         simp only [b, id.def]
@@ -106,7 +108,7 @@ theorem tendsto_sum_pi_div_four :
         rw [← mul_assoc, @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; linarith),
           pow_mul x 2 i, ← mul_pow (-1) (x ^ 2) i]
         ring_nf
-    convert(has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
+    convert (has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
     have g_sum :=
       @geom_sum_eq _ _ (-x ^ 2) ((neg_nonpos.mpr (sq_nonneg x)).trans_lt zero_lt_one).Ne k
     simp only [f'] at g_sum ⊢

f2ce6086

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -109,7 +109,7 @@ theorem tendsto_sum_pi_div_four :
     convert(has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
     have g_sum :=
       @geom_sum_eq _ _ (-x ^ 2) ((neg_nonpos.mpr (sq_nonneg x)).trans_lt zero_lt_one).Ne k
-    simp only [f'] at g_sum⊢
+    simp only [f'] at g_sum ⊢
     rw [g_sum, ← neg_add' (x ^ 2) 1, add_comm (x ^ 2) 1, sub_eq_add_neg, neg_div', neg_div_neg_eq]
     ring
   have hderiv1 : ∀ x ∈ Icc (U : ℝ) 1, HasDerivWithinAt f (f' x) (Icc (U : ℝ) 1) x := fun x hx =>
@@ -130,15 +130,15 @@ theorem tendsto_sum_pi_div_four :
     by
     rintro x ⟨hx_left, hx_right⟩
     have hincr := pow_le_pow_of_le_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
-    rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr
-    rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right
+    rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr 
+    rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right 
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_of_lt hx_right)))]
   have hbound2 : ∀ x ∈ Ico 0 (U : ℝ), |f' x| ≤ U ^ (2 * k) :=
     by
     rintro x ⟨hx_left, hx_right⟩
     have hincr := pow_le_pow_of_le_left hx_left (le_of_lt hx_right) (2 * k)
-    rw [← abs_of_nonneg hx_left] at hincr hx_right
-    rw [← abs_of_nonneg hU2] at hU1 hx_right
+    rw [← abs_of_nonneg hx_left] at hincr hx_right 
+    rw [← abs_of_nonneg hU2] at hU1 hx_right 
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_trans (le_of_lt hx_right) hU1)))]
   -- (6) We twice apply the Mean Value Theorem to obtain bounds on `f` from the bounds on `f'`
   have mvt1 := norm_image_sub_le_of_norm_deriv_le_segment' hderiv1 hbound1 _ (right_mem_Icc.mpr hU1)

f2ce6086

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -17,7 +17,7 @@ namespace Real
 
 open Filter Set
 
-open Classical BigOperators Topology Real
+open scoped Classical BigOperators Topology Real
 
 -- mathport name: abs
 local notation "|" x "|" => abs x

f2ce6086

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -61,9 +61,7 @@ theorem tendsto_sum_pi_div_four :
       simp only [NNReal.coe_nat_cast, Function.comp_apply, NNReal.coe_rpow]
       rw [← rpow_mul (Nat.cast_nonneg k) (-1 / (2 * (k : ℝ) + 1)) (2 * (k : ℝ) + 1),
         @div_mul_cancel _ _ (2 * (k : ℝ) + 1) _
-          (by
-            norm_cast
-            simp only [Nat.succ_ne_zero, not_false_iff]),
+          (by norm_cast; simp only [Nat.succ_ne_zero, not_false_iff]),
         rpow_neg_one k, sub_eq_add_neg]
     · simp only [add_zero, add_right_neg]
   -- (2) We convert the limit in our goal to an inequality
@@ -77,8 +75,7 @@ theorem tendsto_sum_pi_div_four :
   suffices f_bound : |f 1 - f 0| ≤ (1 : ℝ) - U + U ^ (2 * (k : ℝ) + 1)
   · rw [← norm_neg]
     convert f_bound
-    simp only [f]
-    simp [b]
+    simp only [f]; simp [b]
   -- We show that `U` is indeed in [0,1]
   have hU1 : (U : ℝ) ≤ 1 := by
     by_cases hk : k = 0
@@ -86,14 +83,10 @@ theorem tendsto_sum_pi_div_four :
     ·
       exact
         rpow_le_one_of_one_le_of_nonpos
-          (by
-            norm_cast
-            exact nat.succ_le_iff.mpr (Nat.pos_of_ne_zero hk))
+          (by norm_cast; exact nat.succ_le_iff.mpr (Nat.pos_of_ne_zero hk))
           (le_of_lt
             (@div_neg_of_neg_of_pos _ _ (-(1 : ℝ)) (2 * k + 1) (neg_neg_iff_pos.mpr zero_lt_one)
-              (by
-                norm_cast
-                exact Nat.succ_pos')))
+              (by norm_cast; exact Nat.succ_pos')))
   have hU2 := NNReal.coe_nonneg U
   -- (4) We compute the derivative of `f`, denoted by `f'`
   let f' := fun x : ℝ => (-x ^ 2) ^ k / (1 + x ^ 2)
@@ -110,11 +103,7 @@ theorem tendsto_sum_pi_div_four :
         ring
       · simp only [Nat.add_succ_sub_one, add_zero, mul_one, id.def, Nat.cast_bit0, Nat.cast_add,
           Nat.cast_one, Nat.cast_mul]
-        rw [← mul_assoc,
-          @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _
-            (by
-              norm_cast
-              linarith),
+        rw [← mul_assoc, @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; linarith),
           pow_mul x 2 i, ← mul_pow (-1) (x ^ 2) i]
         ring_nf
     convert(has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
@@ -160,10 +149,7 @@ theorem tendsto_sum_pi_div_four :
     _ ≤ 1 * (1 - U) + U ^ (2 * k) * (U - 0) :=
       (le_trans (abs_add (f 1 - f U) (f U - f 0)) (add_le_add mvt1 mvt2))
     _ = 1 - U + U ^ (2 * k) * U := by ring
-    _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) :=
-      by
-      rw [← pow_succ' (U : ℝ) (2 * k)]
-      norm_cast
+    _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) := by rw [← pow_succ' (U : ℝ) (2 * k)]; norm_cast
     
 #align real.tendsto_sum_pi_div_four Real.tendsto_sum_pi_div_four

f2ce6086

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -54,8 +54,7 @@ theorem tendsto_sum_pi_div_four :
   let u := fun k : ℕ => (k : NNReal) ^ (-1 / (2 * (k : ℝ) + 1))
   have H : tendsto (fun k : ℕ => (1 : ℝ) - u k + u k ^ (2 * (k : ℝ) + 1)) at_top (𝓝 0) :=
     by
-    convert
-      (((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
+    convert(((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
             tendsto_inv_atTop_zero).comp
         tendsto_nat_cast_atTop_atTop
     · ext k
@@ -104,8 +103,7 @@ theorem tendsto_sum_pi_div_four :
     have has_deriv_at_b : ∀ i ∈ Finset.range k, HasDerivAt (b i) ((-x ^ 2) ^ i) x :=
       by
       intro i hi
-      convert
-        HasDerivAt.const_mul ((-1 : ℝ) ^ i / (2 * i + 1))
+      convert HasDerivAt.const_mul ((-1 : ℝ) ^ i / (2 * i + 1))
           (@HasDerivAt.pow _ _ _ _ _ (2 * i + 1) (hasDerivAt_id x))
       · ext y
         simp only [b, id.def]
@@ -119,7 +117,7 @@ theorem tendsto_sum_pi_div_four :
               linarith),
           pow_mul x 2 i, ← mul_pow (-1) (x ^ 2) i]
         ring_nf
-    convert (has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
+    convert(has_deriv_at_arctan x).sub (HasDerivAt.sum has_deriv_at_b)
     have g_sum :=
       @geom_sum_eq _ _ (-x ^ 2) ((neg_nonpos.mpr (sq_nonneg x)).trans_lt zero_lt_one).Ne k
     simp only [f'] at g_sum⊢

f2ce6086

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -160,7 +160,7 @@ theorem tendsto_sum_pi_div_four :
   calc
     |f 1 - f 0| = |f 1 - f U + (f U - f 0)| := by ring_nf
     _ ≤ 1 * (1 - U) + U ^ (2 * k) * (U - 0) :=
-      le_trans (abs_add (f 1 - f U) (f U - f 0)) (add_le_add mvt1 mvt2)
+      (le_trans (abs_add (f 1 - f U) (f U - f 0)) (add_le_add mvt1 mvt2))
     _ = 1 - U + U ^ (2 * k) * U := by ring
     _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) :=
       by

f2ce6086

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -26,7 +26,7 @@ theorem tendsto_sum_pi_div_four :
     apply Antitone.tendsto_alternating_series_of_tendsto_zero
     · exact antitone_iff_forall_lt.mpr fun _ _ _ ↦ by gcongr
     · apply Tendsto.inv_tendsto_atTop; apply tendsto_atTop_add_const_right
-      exact tendsto_nat_cast_atTop_atTop.const_mul_atTop zero_lt_two
+      exact tendsto_natCast_atTop_atTop.const_mul_atTop zero_lt_two
   -- Abel's limit theorem states that the corresponding power series has the same limit as `x → 1⁻`
   have abel := tendsto_tsum_powerSeries_nhdsWithin_lt h
   -- Massage the expression to get `x ^ (2 * n + 1)` in the tsum rather than `x ^ n`...

f2ce6086

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -51,7 +51,7 @@ theorem tendsto_sum_pi_div_four :
     rw [Set.mem_Iio] at hy2
     have ny : ‖y‖ < 1 := by rw [norm_eq_abs, abs_lt]; constructor <;> linarith
     rw [← (hasSum_arctan ny).tsum_eq, Function.comp_apply, ← tsum_mul_right]
-    simp_rw [mul_assoc, ← pow_mul, ← pow_succ', div_mul_eq_mul_div]
+    simp_rw [mul_assoc, ← pow_mul, ← pow_succ, div_mul_eq_mul_div]
     norm_cast
   -- But `arctan` is continuous everywhere, so the limit is `arctan 1 = π / 4`
   rwa [tendsto_nhds_unique abel ((continuous_arctan.tendsto 1).mono_left m), arctan_one] at h

f2ce6086

chore: change authorship of Leibniz series proof (#11578)

9764de80

Diff

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2020 Benjamin Davidson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Benjamin Davidson
+Authors: Benjamin Davidson, Jeremy Tan
 -/
 import Mathlib.Analysis.Complex.AbelLimit
 import Mathlib.Analysis.SpecialFunctions.Complex.Arctan

f2ce6086

feat: prove Leibniz π series with Abel's limit theorem (#11098)

This resolves the Zulip comment here.

c0210180

Diff

@@ -3,136 +3,58 @@ Copyright (c) 2020 Benjamin Davidson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Benjamin Davidson
 -/
-import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
-import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
+import Mathlib.Analysis.Complex.AbelLimit
+import Mathlib.Analysis.SpecialFunctions.Complex.Arctan
 
 #align_import data.real.pi.leibniz from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 
-/-! ### Leibniz's Series for Pi -/
-
+/-! ### Leibniz's series for `π` -/
 
 namespace Real
 
-open Filter Set
-
-open scoped Classical BigOperators Topology Real
-
-/-- This theorem establishes **Leibniz's series for `π`**: The alternating sum of the reciprocals
-  of the odd numbers is `π/4`. Note that this is a conditionally rather than absolutely convergent
-  series. The main tool that this proof uses is the Mean Value Theorem (specifically avoiding the
-  Fundamental Theorem of Calculus).
-
-  Intuitively, the theorem holds because Leibniz's series is the Taylor series of `arctan x`
-  centered about `0` and evaluated at the value `x = 1`. Therefore, much of this proof consists of
-  reasoning about a function
-    `f := arctan x - ∑ i in Finset.range k, (-(1:ℝ))^i * x^(2*i+1) / (2*i+1)`,
-  the difference between `arctan` and the `k`-th partial sum of its Taylor series. Some ingenuity is
-  required due to the fact that the Taylor series is not absolutely convergent at `x = 1`.
+open Filter Finset
 
-  This proof requires a bound on `f 1`, the key idea being that `f 1` can be split as the sum of
-  `f 1 - f u` and `f u`, where `u` is a sequence of values in [0,1], carefully chosen such that
-  each of these two terms can be controlled (in different ways).
+open scoped BigOperators Topology
 
-  We begin the proof by (1) introducing that sequence `u` and then proving that another sequence
-  constructed from `u` tends to `0` at `+∞`. After (2) converting the limit in our goal to an
-  inequality, we (3) introduce the auxiliary function `f` defined above. Next, we (4) compute the
-  derivative of `f`, denoted by `f'`, first generally and then on each of two subintervals of [0,1].
-  We then (5) prove a bound for `f'`, again both generally as well as on each of the two
-  subintervals. Finally, we (6) apply the Mean Value Theorem twice, obtaining bounds on `f 1 - f u`
-  and `f u - f 0` from the bounds on `f'` (note that `f 0 = 0`). -/
+/-- **Leibniz's series for `π`**. The alternating sum of odd number reciprocals is `π / 4`,
+proved by using Abel's limit theorem to extend the Maclaurin series of `arctan` to 1. -/
 theorem tendsto_sum_pi_div_four :
-    Tendsto (fun k => ∑ i in Finset.range k, (-(1 : ℝ)) ^ i / (2 * i + 1)) atTop (𝓝 (π / 4)) := by
-  rw [tendsto_iff_norm_sub_tendsto_zero, ← tendsto_zero_iff_norm_tendsto_zero]
-  -- (1) We introduce a useful sequence `u` of values in [0,1], then prove that another sequence
-  --     constructed from `u` tends to `0` at `+∞`
-  let u := fun k : ℕ => (k : NNReal) ^ (-1 / (2 * (k : ℝ) + 1))
-  have H : Tendsto (fun k : ℕ => (1 : ℝ) - u k + u k ^ (2 * (k : ℝ) + 1)) atTop (𝓝 0) := by
-    convert (((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
-        tendsto_inv_atTop_zero).comp tendsto_nat_cast_atTop_atTop using 1
-    · ext k
-      simp only [u, NNReal.coe_nat_cast, Function.comp_apply, NNReal.coe_rpow]
-      rw [← rpow_mul (Nat.cast_nonneg k) (-1 / (2 * (k : ℝ) + 1)) (2 * (k : ℝ) + 1),
-        @div_mul_cancel _ _ (2 * (k : ℝ) + 1) _
-          (by norm_cast; simp only [Nat.succ_ne_zero, not_false_iff]),
-        rpow_neg_one k, sub_eq_add_neg]
-    · simp only [add_zero, add_right_neg]
-  -- (2) We convert the limit in our goal to an inequality
-  refine' squeeze_zero_norm _ H
-  intro k
-  -- Since `k` is now fixed, we henceforth denote `u k` as `U`
-  let U := u k
-  -- (3) We introduce an auxiliary function `f`
-  let b (i : ℕ) x := (-(1 : ℝ)) ^ i * x ^ (2 * i + 1) / (2 * i + 1)
-  let f x := arctan x - ∑ i in Finset.range k, b i x
-  suffices f_bound : |f 1 - f 0| ≤ (1 : ℝ) - U + U ^ (2 * (k : ℝ) + 1) by
-    rw [← norm_neg]
-    convert f_bound using 1
-    simp [b, f]
-  -- We show that `U` is indeed in [0,1]
-  have hU1 : (U : ℝ) ≤ 1 := by
-    by_cases hk : k = 0
-    · simp [U, u, hk]
-    · exact rpow_le_one_of_one_le_of_nonpos
-        (by norm_cast; exact Nat.succ_le_iff.mpr (Nat.pos_of_ne_zero hk)) (le_of_lt
-          (@div_neg_of_neg_of_pos _ _ (-(1 : ℝ)) (2 * k + 1) (neg_neg_iff_pos.mpr zero_lt_one)
-            (by norm_cast; exact Nat.succ_pos')))
-  have hU2 := NNReal.coe_nonneg U
-  -- (4) We compute the derivative of `f`, denoted by `f'`
-  let f' := fun x : ℝ => (-x ^ 2) ^ k / (1 + x ^ 2)
-  have has_deriv_at_f : ∀ x, HasDerivAt f (f' x) x := by
-    intro x
-    have has_deriv_at_b : ∀ i ∈ Finset.range k, HasDerivAt (b i) ((-x ^ 2) ^ i) x := by
-      intro i _
-      convert HasDerivAt.const_mul ((-1 : ℝ) ^ i / (2 * i + 1))
-          (HasDerivAt.pow (2 * i + 1) (hasDerivAt_id x)) using 1
-      · ext y
-        simp only [id.def]
-        ring
-      · simp
-        rw [← mul_assoc, @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; omega),
-          pow_mul x 2 i, ← mul_pow (-1 : ℝ) (x ^ 2) i]
-        ring_nf
-    convert (hasDerivAt_arctan x).sub (HasDerivAt.sum has_deriv_at_b) using 1
-    have g_sum :=
-      @geom_sum_eq _ _ (-x ^ 2) ((neg_nonpos.mpr (sq_nonneg x)).trans_lt zero_lt_one).ne k
-    simp only at g_sum ⊢
-    rw [g_sum, ← neg_add' (x ^ 2) 1, add_comm (x ^ 2) 1, sub_eq_add_neg, neg_div', neg_div_neg_eq]
-    ring
-  have hderiv1 : ∀ x ∈ Icc (U : ℝ) 1, HasDerivWithinAt f (f' x) (Icc (U : ℝ) 1) x := fun x _ =>
-    (has_deriv_at_f x).hasDerivWithinAt
-  have hderiv2 : ∀ x ∈ Icc 0 (U : ℝ), HasDerivWithinAt f (f' x) (Icc 0 (U : ℝ)) x := fun x _ =>
-    (has_deriv_at_f x).hasDerivWithinAt
-  -- (5) We prove a general bound for `f'` and then more precise bounds on each of two subintervals
-  have f'_bound : ∀ x ∈ Icc (-1 : ℝ) 1, |f' x| ≤ |x| ^ (2 * k) := by
-    intro x _
-    rw [abs_div, IsAbsoluteValue.abv_pow abs (-x ^ 2) k, abs_neg, IsAbsoluteValue.abv_pow abs x 2,
-      ← pow_mul]
-    refine' div_le_of_nonneg_of_le_mul (abs_nonneg _) (pow_nonneg (abs_nonneg _) _) _
-    refine' le_mul_of_one_le_right (pow_nonneg (abs_nonneg _) _) _
-    rw_mod_cast [abs_of_nonneg (add_nonneg zero_le_one (sq_nonneg x) : (0 : ℝ) ≤ _)]
-    exact (le_add_of_nonneg_right (sq_nonneg x) : (1 : ℝ) ≤ _)
-  have hbound1 : ∀ x ∈ Ico (U : ℝ) 1, |f' x| ≤ 1 := by
-    rintro x ⟨hx_left, hx_right⟩
-    have hincr := pow_le_pow_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
-    rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr
-    rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right
-    linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_of_lt hx_right)))]
-  have hbound2 : ∀ x ∈ Ico 0 (U : ℝ), |f' x| ≤ U ^ (2 * k) := by
-    rintro x ⟨hx_left, hx_right⟩
-    have hincr := pow_le_pow_left hx_left (le_of_lt hx_right) (2 * k)
-    rw [← abs_of_nonneg hx_left] at hincr hx_right
-    rw [← abs_of_nonneg hU2] at hU1 hx_right
-    exact (f'_bound x (mem_Icc.mpr (abs_le.mp (le_trans (le_of_lt hx_right) hU1)))).trans hincr
-  -- (6) We twice apply the Mean Value Theorem to obtain bounds on `f` from the bounds on `f'`
-  have mvt1 := norm_image_sub_le_of_norm_deriv_le_segment' hderiv1 hbound1 _ (right_mem_Icc.mpr hU1)
-  have mvt2 := norm_image_sub_le_of_norm_deriv_le_segment' hderiv2 hbound2 _ (right_mem_Icc.mpr hU2)
-  -- The following algebra is enough to complete the proof
-  calc
-    |f 1 - f 0| = |f 1 - f U + (f U - f 0)| := by simp
-    _ ≤ 1 * (1 - U) + U ^ (2 * k) * (U - 0) :=
-      (le_trans (abs_add (f 1 - f U) (f U - f 0)) (add_le_add mvt1 mvt2))
-    _ = 1 - U + (U : ℝ) ^ (2 * k) * U := by simp
-    _ = 1 - u k + u k ^ (2 * (k : ℝ) + 1) := by rw [← pow_succ' (U : ℝ) (2 * k)]; norm_cast
+    Tendsto (fun k => ∑ i in range k, (-1 : ℝ) ^ i / (2 * i + 1)) atTop (𝓝 (π / 4)) := by
+  -- The series is alternating with terms of decreasing magnitude, so it converges to some limit
+  obtain ⟨l, h⟩ :
+      ∃ l, Tendsto (fun n ↦ ∑ i in range n, (-1 : ℝ) ^ i / (2 * i + 1)) atTop (𝓝 l) := by
+    apply Antitone.tendsto_alternating_series_of_tendsto_zero
+    · exact antitone_iff_forall_lt.mpr fun _ _ _ ↦ by gcongr
+    · apply Tendsto.inv_tendsto_atTop; apply tendsto_atTop_add_const_right
+      exact tendsto_nat_cast_atTop_atTop.const_mul_atTop zero_lt_two
+  -- Abel's limit theorem states that the corresponding power series has the same limit as `x → 1⁻`
+  have abel := tendsto_tsum_powerSeries_nhdsWithin_lt h
+  -- Massage the expression to get `x ^ (2 * n + 1)` in the tsum rather than `x ^ n`...
+  have m : 𝓝[<] (1 : ℝ) ≤ 𝓝 1 := tendsto_nhdsWithin_of_tendsto_nhds fun _ a ↦ a
+  have q : Tendsto (fun x : ℝ ↦ x ^ 2) (𝓝[<] 1) (𝓝[<] 1) := by
+    apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
+    · nth_rw 3 [← one_pow 2]
+      exact Tendsto.pow ‹_› _
+    · rw [eventually_iff_exists_mem]
+      use Set.Ioo (-1) 1
+      exact ⟨(by rw [mem_nhdsWithin_Iio_iff_exists_Ioo_subset]; use -1, by simp),
+        fun _ _ ↦ by rwa [Set.mem_Iio, sq_lt_one_iff_abs_lt_one, abs_lt, ← Set.mem_Ioo]⟩
+  replace abel := (abel.comp q).mul m
+  rw [mul_one] at abel
+  -- ...so that we can replace the tsum with the real arctangent function
+  replace abel : Tendsto arctan (𝓝[<] 1) (𝓝 l) := by
+    apply abel.congr'
+    rw [eventuallyEq_nhdsWithin_iff, Metric.eventually_nhds_iff]
+    use 1, zero_lt_one
+    intro y hy1 hy2
+    rw [dist_eq, abs_sub_lt_iff] at hy1
+    rw [Set.mem_Iio] at hy2
+    have ny : ‖y‖ < 1 := by rw [norm_eq_abs, abs_lt]; constructor <;> linarith
+    rw [← (hasSum_arctan ny).tsum_eq, Function.comp_apply, ← tsum_mul_right]
+    simp_rw [mul_assoc, ← pow_mul, ← pow_succ', div_mul_eq_mul_div]
+    norm_cast
+  -- But `arctan` is continuous everywhere, so the limit is `arctan 1 = π / 4`
+  rwa [tendsto_nhds_unique abel ((continuous_arctan.tendsto 1).mono_left m), arctan_one] at h
 #align real.tendsto_sum_pi_div_four Real.tendsto_sum_pi_div_four
 
 end Real

f2ce6086

refactor: optimize proofs with omega (#11093)

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

37bc4aba

Diff

@@ -89,7 +89,7 @@ theorem tendsto_sum_pi_div_four :
         simp only [id.def]
         ring
       · simp
-        rw [← mul_assoc, @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; linarith),
+        rw [← mul_assoc, @div_mul_cancel _ _ (2 * (i : ℝ) + 1) _ (by norm_cast; omega),
           pow_mul x 2 i, ← mul_pow (-1 : ℝ) (x ^ 2) i]
         ring_nf
     convert (hasDerivAt_arctan x).sub (HasDerivAt.sum has_deriv_at_b) using 1

f2ce6086

chore: prepare Lean version bump with explicit simp (#10999)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

38bce757

Diff

@@ -50,7 +50,7 @@ theorem tendsto_sum_pi_div_four :
     convert (((tendsto_rpow_div_mul_add (-1) 2 1 two_ne_zero.symm).neg.const_add 1).add
         tendsto_inv_atTop_zero).comp tendsto_nat_cast_atTop_atTop using 1
     · ext k
-      simp only [NNReal.coe_nat_cast, Function.comp_apply, NNReal.coe_rpow]
+      simp only [u, NNReal.coe_nat_cast, Function.comp_apply, NNReal.coe_rpow]
       rw [← rpow_mul (Nat.cast_nonneg k) (-1 / (2 * (k : ℝ) + 1)) (2 * (k : ℝ) + 1),
         @div_mul_cancel _ _ (2 * (k : ℝ) + 1) _
           (by norm_cast; simp only [Nat.succ_ne_zero, not_false_iff]),
@@ -67,11 +67,11 @@ theorem tendsto_sum_pi_div_four :
   suffices f_bound : |f 1 - f 0| ≤ (1 : ℝ) - U + U ^ (2 * (k : ℝ) + 1) by
     rw [← norm_neg]
     convert f_bound using 1
-    simp
+    simp [b, f]
   -- We show that `U` is indeed in [0,1]
   have hU1 : (U : ℝ) ≤ 1 := by
     by_cases hk : k = 0
-    · simp [hk]
+    · simp [U, u, hk]
     · exact rpow_le_one_of_one_le_of_nonpos
         (by norm_cast; exact Nat.succ_le_iff.mpr (Nat.pos_of_ne_zero hk)) (le_of_lt
           (@div_neg_of_neg_of_pos _ _ (-(1 : ℝ)) (2 * k + 1) (neg_neg_iff_pos.mpr zero_lt_one)

f2ce6086

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -64,8 +64,8 @@ theorem tendsto_sum_pi_div_four :
   -- (3) We introduce an auxiliary function `f`
   let b (i : ℕ) x := (-(1 : ℝ)) ^ i * x ^ (2 * i + 1) / (2 * i + 1)
   let f x := arctan x - ∑ i in Finset.range k, b i x
-  suffices f_bound : |f 1 - f 0| ≤ (1 : ℝ) - U + U ^ (2 * (k : ℝ) + 1)
-  · rw [← norm_neg]
+  suffices f_bound : |f 1 - f 0| ≤ (1 : ℝ) - U + U ^ (2 * (k : ℝ) + 1) by
+    rw [← norm_neg]
     convert f_bound using 1
     simp
   -- We show that `U` is indeed in [0,1]

f2ce6086

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Benjamin Davidson
 -/
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
+import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
 
 #align_import data.real.pi.leibniz from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

f2ce6086

chore: Rename pow monotonicity lemmas (#9095)

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

`Algebra.GroupPower.Order`

pow_mono → pow_right_mono
pow_le_pow → pow_le_pow_right
pow_le_pow_of_le_left → pow_le_pow_left
pow_lt_pow_of_lt_left → pow_lt_pow_left
strictMonoOn_pow → pow_left_strictMonoOn
pow_strictMono_right → pow_right_strictMono
pow_lt_pow → pow_lt_pow_right
pow_lt_pow_iff → pow_lt_pow_iff_right
pow_le_pow_iff → pow_le_pow_iff_right
self_lt_pow → lt_self_pow
strictAnti_pow → pow_right_strictAnti
pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
le_of_pow_le_pow → le_of_pow_le_pow_left
pow_lt_pow₀ → pow_lt_pow_right₀

`Algebra.GroupPower.CovariantClass`

pow_le_pow_of_le_left' → pow_le_pow_left'
nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
pow_lt_pow' → pow_lt_pow_right'
nsmul_lt_nsmul → nsmul_lt_nsmul_left
pow_strictMono_left → pow_right_strictMono'
nsmul_strictMono_right → nsmul_left_strictMono
StrictMono.pow_right' → StrictMono.pow_const
StrictMono.nsmul_left → StrictMono.const_nsmul
pow_strictMono_right' → pow_left_strictMono
nsmul_strictMono_left → nsmul_right_strictMono
Monotone.pow_right → Monotone.pow_const
Monotone.nsmul_left → Monotone.const_nsmul
lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
pow_le_pow' → pow_le_pow_right'
nsmul_le_nsmul → nsmul_le_nsmul_left
pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow' → le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
pow_le_pow_iff' → pow_le_pow_iff_right'
nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
pow_lt_pow_iff' → pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

`Data.Nat.Pow`

Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

self_le_pow was a duplicate of le_self_pow.
Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
Nat.pow_right_strictMono is defeq to pow_right_strictMono.
Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

A bunch of proofs have been golfed.
Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
A few Nat lemmas have been protected.
One docstring has been fixed.

d61c95e1

Diff

@@ -112,13 +112,13 @@ theorem tendsto_sum_pi_div_four :
     exact (le_add_of_nonneg_right (sq_nonneg x) : (1 : ℝ) ≤ _)
   have hbound1 : ∀ x ∈ Ico (U : ℝ) 1, |f' x| ≤ 1 := by
     rintro x ⟨hx_left, hx_right⟩
-    have hincr := pow_le_pow_of_le_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
+    have hincr := pow_le_pow_left (le_trans hU2 hx_left) (le_of_lt hx_right) (2 * k)
     rw [one_pow (2 * k), ← abs_of_nonneg (le_trans hU2 hx_left)] at hincr
     rw [← abs_of_nonneg (le_trans hU2 hx_left)] at hx_right
     linarith [f'_bound x (mem_Icc.mpr (abs_le.mp (le_of_lt hx_right)))]
   have hbound2 : ∀ x ∈ Ico 0 (U : ℝ), |f' x| ≤ U ^ (2 * k) := by
     rintro x ⟨hx_left, hx_right⟩
-    have hincr := pow_le_pow_of_le_left hx_left (le_of_lt hx_right) (2 * k)
+    have hincr := pow_le_pow_left hx_left (le_of_lt hx_right) (2 * k)
     rw [← abs_of_nonneg hx_left] at hincr hx_right
     rw [← abs_of_nonneg hU2] at hU1 hx_right
     exact (f'_bound x (mem_Icc.mpr (abs_le.mp (le_trans (le_of_lt hx_right) hU1)))).trans hincr

f2ce6086

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -12,8 +12,6 @@ import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
 
 namespace Real
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open Filter Set
 
 open scoped Classical BigOperators Topology Real

f2ce6086

fix(Analysis,Topology): fix names (#6938)

Rename:

tendsto_iff_norm_tendsto_one → tendsto_iff_norm_div_tendsto_zero;
tendsto_iff_norm_tendsto_zero → tendsto_iff_norm_sub_tendsto_zero;
tendsto_one_iff_norm_tendsto_one → tendsto_one_iff_norm_tendsto_zero;
Filter.Tendsto.continuous_of_equicontinuous_at → Filter.Tendsto.continuous_of_equicontinuousAt.

04d2f7d8

Diff

@@ -43,7 +43,7 @@ open scoped Classical BigOperators Topology Real
   and `f u - f 0` from the bounds on `f'` (note that `f 0 = 0`). -/
 theorem tendsto_sum_pi_div_four :
     Tendsto (fun k => ∑ i in Finset.range k, (-(1 : ℝ)) ^ i / (2 * i + 1)) atTop (𝓝 (π / 4)) := by
-  rw [tendsto_iff_norm_tendsto_zero, ← tendsto_zero_iff_norm_tendsto_zero]
+  rw [tendsto_iff_norm_sub_tendsto_zero, ← tendsto_zero_iff_norm_tendsto_zero]
   -- (1) We introduce a useful sequence `u` of values in [0,1], then prove that another sequence
   --     constructed from `u` tends to `0` at `+∞`
   let u := fun k : ℕ => (k : NNReal) ^ (-1 / (2 * (k : ℝ) + 1))

f2ce6086

chore: regularize HPow.hPow porting notes (#6465)

0f85d19f

Diff

@@ -12,7 +12,7 @@ import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
 
 namespace Real
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 open Filter Set

f2ce6086

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Benjamin Davidson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Benjamin Davidson
-
-! This file was ported from Lean 3 source module data.real.pi.leibniz
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
 
+#align_import data.real.pi.leibniz from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-! ### Leibniz's Series for Pi -/

f2ce6086

feat: port Data.Real.Pi.Leibniz (#4766)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

311f1ba0

`data.real.pi.leibniz` ⟷ `Mathlib.Data.Real.Pi.Leibniz`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`

Lemmas added

Lemmas removed

Other changes

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 12 + 950

data.real.pi.leibniz ⟷ Mathlib.Data.Real.Pi.Leibniz

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Algebra.GroupPower.Order

Algebra.GroupPower.CovariantClass

Data.Nat.Pow

Lemmas added

Lemmas removed

Other changes

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 12 + 950

`data.real.pi.leibniz` ⟷ `Mathlib.Data.Real.Pi.Leibniz`

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`