analysis.special_functions.trigonometric.inverse_deriv

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

36938f77

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -121,7 +121,7 @@ theorem differentiableWithinAt_arcsin_Iic {x : ℝ} :
     DifferentiableWithinAt ℝ arcsin (Iic x) x ↔ x ≠ 1 :=
   by
   refine' ⟨fun h => _, fun h => (has_deriv_within_at_arcsin_Iic h).DifferentiableWithinAt⟩
-  rw [← neg_neg x, ← image_neg_Ici] at h 
+  rw [← neg_neg x, ← image_neg_Ici] at h
   have := (h.comp (-x) differentiable_within_at_id.neg (maps_to_image _ _)).neg
   simpa [(· ∘ ·), differentiable_within_at_arcsin_Ici] using this
 #align real.differentiable_within_at_arcsin_Iic Real.differentiableWithinAt_arcsin_Iic
@@ -144,7 +144,7 @@ theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) :=
   by_cases h : x ≠ -1 ∧ x ≠ 1
   · exact (has_deriv_at_arcsin h.1 h.2).deriv
   · rw [deriv_zero_of_not_differentiableAt (mt differentiable_at_arcsin.1 h)]
-    simp only [not_and_or, Ne.def, Classical.not_not] at h 
+    simp only [not_and_or, Ne.def, Classical.not_not] at h
     rcases h with (rfl | rfl) <;> simp
 #align real.deriv_arcsin Real.deriv_arcsin
 -/

36938f77

bump to nightly-2023-11-05-06

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

acc3325f

Diff

@@ -165,7 +165,7 @@ theorem contDiffOn_arcsin {n : ℕ∞} : ContDiffOn ℝ n arcsin ({-1, 1}ᶜ) :=
 #print Real.contDiffAt_arcsin_iff /-
 theorem contDiffAt_arcsin_iff {x : ℝ} {n : ℕ∞} : ContDiffAt ℝ n arcsin x ↔ n = 0 ∨ x ≠ -1 ∧ x ≠ 1 :=
   ⟨fun h =>
-    or_iff_not_imp_left.2 fun hn =>
+    Classical.or_iff_not_imp_left.2 fun hn =>
       differentiableAt_arcsin.1 <| h.DifferentiableAt <| ENat.one_le_iff_ne_zero.2 hn,
     fun h =>
     h.elim (fun hn => hn.symm ▸ (contDiff_zero.2 continuous_arcsin).ContDiffAt) fun hx =>

36938f77

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
 -/
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Inverse
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Deriv
+import Analysis.SpecialFunctions.Trigonometric.Inverse
+import Analysis.SpecialFunctions.Trigonometric.Deriv
 
 #align_import analysis.special_functions.trigonometric.inverse_deriv from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"

36938f77

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.inverse_deriv
-! 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.Analysis.SpecialFunctions.Trigonometric.Inverse
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.Deriv
 
+#align_import analysis.special_functions.trigonometric.inverse_deriv from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # derivatives of the inverse trigonometric functions

36938f77

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -33,6 +33,7 @@ namespace Real
 
 section Arcsin
 
+#print Real.deriv_arcsin_aux /-
 theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
     HasStrictDerivAt arcsin (1 / sqrt (1 - x ^ 2)) x ∧ ContDiffAt ℝ ⊤ arcsin x :=
   by
@@ -58,21 +59,29 @@ theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
       ⟨(hasStrictDerivAt_const _ _).congr_of_eventuallyEq this.symm,
         cont_diff_at_const.congr_of_eventually_eq this⟩
 #align real.deriv_arcsin_aux Real.deriv_arcsin_aux
+-/
 
+#print Real.hasStrictDerivAt_arcsin /-
 theorem hasStrictDerivAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
     HasStrictDerivAt arcsin (1 / sqrt (1 - x ^ 2)) x :=
   (deriv_arcsin_aux h₁ h₂).1
 #align real.has_strict_deriv_at_arcsin Real.hasStrictDerivAt_arcsin
+-/
 
+#print Real.hasDerivAt_arcsin /-
 theorem hasDerivAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
     HasDerivAt arcsin (1 / sqrt (1 - x ^ 2)) x :=
   (hasStrictDerivAt_arcsin h₁ h₂).HasDerivAt
 #align real.has_deriv_at_arcsin Real.hasDerivAt_arcsin
+-/
 
+#print Real.contDiffAt_arcsin /-
 theorem contDiffAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) {n : ℕ∞} : ContDiffAt ℝ n arcsin x :=
   (deriv_arcsin_aux h₁ h₂).2.of_le le_top
 #align real.cont_diff_at_arcsin Real.contDiffAt_arcsin
+-/
 
+#print Real.hasDerivWithinAt_arcsin_Ici /-
 theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
     HasDerivWithinAt arcsin (1 / sqrt (1 - x ^ 2)) (Ici x) x :=
   by
@@ -82,7 +91,9 @@ theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
       simp (config := { contextual := true }) [arcsin_of_one_le]
   · exact (has_deriv_at_arcsin h h').HasDerivWithinAt
 #align real.has_deriv_within_at_arcsin_Ici Real.hasDerivWithinAt_arcsin_Ici
+-/
 
+#print Real.hasDerivWithinAt_arcsin_Iic /-
 theorem hasDerivWithinAt_arcsin_Iic {x : ℝ} (h : x ≠ 1) :
     HasDerivWithinAt arcsin (1 / sqrt (1 - x ^ 2)) (Iic x) x :=
   by
@@ -92,7 +103,9 @@ theorem hasDerivWithinAt_arcsin_Iic {x : ℝ} (h : x ≠ 1) :
       simp (config := { contextual := true }) [arcsin_of_le_neg_one]
   · exact (has_deriv_at_arcsin h' h).HasDerivWithinAt
 #align real.has_deriv_within_at_arcsin_Iic Real.hasDerivWithinAt_arcsin_Iic
+-/
 
+#print Real.differentiableWithinAt_arcsin_Ici /-
 theorem differentiableWithinAt_arcsin_Ici {x : ℝ} :
     DifferentiableWithinAt ℝ arcsin (Ici x) x ↔ x ≠ -1 :=
   by
@@ -104,7 +117,9 @@ theorem differentiableWithinAt_arcsin_Ici {x : ℝ} :
   have := h.has_deriv_within_at.sin.congr_of_eventually_eq this.symm (by simp)
   simpa using (uniqueDiffOn_Ici _ _ left_mem_Ici).eq_deriv _ this (hasDerivWithinAt_id _ _)
 #align real.differentiable_within_at_arcsin_Ici Real.differentiableWithinAt_arcsin_Ici
+-/
 
+#print Real.differentiableWithinAt_arcsin_Iic /-
 theorem differentiableWithinAt_arcsin_Iic {x : ℝ} :
     DifferentiableWithinAt ℝ arcsin (Iic x) x ↔ x ≠ 1 :=
   by
@@ -113,14 +128,18 @@ theorem differentiableWithinAt_arcsin_Iic {x : ℝ} :
   have := (h.comp (-x) differentiable_within_at_id.neg (maps_to_image _ _)).neg
   simpa [(· ∘ ·), differentiable_within_at_arcsin_Ici] using this
 #align real.differentiable_within_at_arcsin_Iic Real.differentiableWithinAt_arcsin_Iic
+-/
 
+#print Real.differentiableAt_arcsin /-
 theorem differentiableAt_arcsin {x : ℝ} : DifferentiableAt ℝ arcsin x ↔ x ≠ -1 ∧ x ≠ 1 :=
   ⟨fun h =>
     ⟨differentiableWithinAt_arcsin_Ici.1 h.DifferentiableWithinAt,
       differentiableWithinAt_arcsin_Iic.1 h.DifferentiableWithinAt⟩,
     fun h => (hasDerivAt_arcsin h.1 h.2).DifferentiableAt⟩
 #align real.differentiable_at_arcsin Real.differentiableAt_arcsin
+-/
 
+#print Real.deriv_arcsin /-
 @[simp]
 theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) :=
   by
@@ -131,16 +150,22 @@ theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) :=
     simp only [not_and_or, Ne.def, Classical.not_not] at h 
     rcases h with (rfl | rfl) <;> simp
 #align real.deriv_arcsin Real.deriv_arcsin
+-/
 
+#print Real.differentiableOn_arcsin /-
 theorem differentiableOn_arcsin : DifferentiableOn ℝ arcsin ({-1, 1}ᶜ) := fun x hx =>
   (differentiableAt_arcsin.2
       ⟨fun h => hx (Or.inl h), fun h => hx (Or.inr h)⟩).DifferentiableWithinAt
 #align real.differentiable_on_arcsin Real.differentiableOn_arcsin
+-/
 
+#print Real.contDiffOn_arcsin /-
 theorem contDiffOn_arcsin {n : ℕ∞} : ContDiffOn ℝ n arcsin ({-1, 1}ᶜ) := fun x hx =>
   (contDiffAt_arcsin (mt Or.inl hx) (mt Or.inr hx)).ContDiffWithinAt
 #align real.cont_diff_on_arcsin Real.contDiffOn_arcsin
+-/
 
+#print Real.contDiffAt_arcsin_iff /-
 theorem contDiffAt_arcsin_iff {x : ℝ} {n : ℕ∞} : ContDiffAt ℝ n arcsin x ↔ n = 0 ∨ x ≠ -1 ∧ x ≠ 1 :=
   ⟨fun h =>
     or_iff_not_imp_left.2 fun hn =>
@@ -149,67 +174,92 @@ theorem contDiffAt_arcsin_iff {x : ℝ} {n : ℕ∞} : ContDiffAt ℝ n arcsin x
     h.elim (fun hn => hn.symm ▸ (contDiff_zero.2 continuous_arcsin).ContDiffAt) fun hx =>
       contDiffAt_arcsin hx.1 hx.2⟩
 #align real.cont_diff_at_arcsin_iff Real.contDiffAt_arcsin_iff
+-/
 
 end Arcsin
 
 section Arccos
 
+#print Real.hasStrictDerivAt_arccos /-
 theorem hasStrictDerivAt_arccos {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
     HasStrictDerivAt arccos (-(1 / sqrt (1 - x ^ 2))) x :=
   (hasStrictDerivAt_arcsin h₁ h₂).const_sub (π / 2)
 #align real.has_strict_deriv_at_arccos Real.hasStrictDerivAt_arccos
+-/
 
+#print Real.hasDerivAt_arccos /-
 theorem hasDerivAt_arccos {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
     HasDerivAt arccos (-(1 / sqrt (1 - x ^ 2))) x :=
   (hasDerivAt_arcsin h₁ h₂).const_sub (π / 2)
 #align real.has_deriv_at_arccos Real.hasDerivAt_arccos
+-/
 
+#print Real.contDiffAt_arccos /-
 theorem contDiffAt_arccos {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) {n : ℕ∞} : ContDiffAt ℝ n arccos x :=
   contDiffAt_const.sub (contDiffAt_arcsin h₁ h₂)
 #align real.cont_diff_at_arccos Real.contDiffAt_arccos
+-/
 
+#print Real.hasDerivWithinAt_arccos_Ici /-
 theorem hasDerivWithinAt_arccos_Ici {x : ℝ} (h : x ≠ -1) :
     HasDerivWithinAt arccos (-(1 / sqrt (1 - x ^ 2))) (Ici x) x :=
   (hasDerivWithinAt_arcsin_Ici h).const_sub _
 #align real.has_deriv_within_at_arccos_Ici Real.hasDerivWithinAt_arccos_Ici
+-/
 
+#print Real.hasDerivWithinAt_arccos_Iic /-
 theorem hasDerivWithinAt_arccos_Iic {x : ℝ} (h : x ≠ 1) :
     HasDerivWithinAt arccos (-(1 / sqrt (1 - x ^ 2))) (Iic x) x :=
   (hasDerivWithinAt_arcsin_Iic h).const_sub _
 #align real.has_deriv_within_at_arccos_Iic Real.hasDerivWithinAt_arccos_Iic
+-/
 
+#print Real.differentiableWithinAt_arccos_Ici /-
 theorem differentiableWithinAt_arccos_Ici {x : ℝ} :
     DifferentiableWithinAt ℝ arccos (Ici x) x ↔ x ≠ -1 :=
   (differentiableWithinAt_const_sub_iff _).trans differentiableWithinAt_arcsin_Ici
 #align real.differentiable_within_at_arccos_Ici Real.differentiableWithinAt_arccos_Ici
+-/
 
+#print Real.differentiableWithinAt_arccos_Iic /-
 theorem differentiableWithinAt_arccos_Iic {x : ℝ} :
     DifferentiableWithinAt ℝ arccos (Iic x) x ↔ x ≠ 1 :=
   (differentiableWithinAt_const_sub_iff _).trans differentiableWithinAt_arcsin_Iic
 #align real.differentiable_within_at_arccos_Iic Real.differentiableWithinAt_arccos_Iic
+-/
 
+#print Real.differentiableAt_arccos /-
 theorem differentiableAt_arccos {x : ℝ} : DifferentiableAt ℝ arccos x ↔ x ≠ -1 ∧ x ≠ 1 :=
   (differentiableAt_const_sub_iff _).trans differentiableAt_arcsin
 #align real.differentiable_at_arccos Real.differentiableAt_arccos
+-/
 
+#print Real.deriv_arccos /-
 @[simp]
 theorem deriv_arccos : deriv arccos = fun x => -(1 / sqrt (1 - x ^ 2)) :=
   funext fun x => (deriv_const_sub _).trans <| by simp only [deriv_arcsin]
 #align real.deriv_arccos Real.deriv_arccos
+-/
 
+#print Real.differentiableOn_arccos /-
 theorem differentiableOn_arccos : DifferentiableOn ℝ arccos ({-1, 1}ᶜ) :=
   differentiableOn_arcsin.const_sub _
 #align real.differentiable_on_arccos Real.differentiableOn_arccos
+-/
 
+#print Real.contDiffOn_arccos /-
 theorem contDiffOn_arccos {n : ℕ∞} : ContDiffOn ℝ n arccos ({-1, 1}ᶜ) :=
   contDiffOn_const.sub contDiffOn_arcsin
 #align real.cont_diff_on_arccos Real.contDiffOn_arccos
+-/
 
+#print Real.contDiffAt_arccos_iff /-
 theorem contDiffAt_arccos_iff {x : ℝ} {n : ℕ∞} : ContDiffAt ℝ n arccos x ↔ n = 0 ∨ x ≠ -1 ∧ x ≠ 1 :=
   by
   refine' Iff.trans ⟨fun h => _, fun h => _⟩ cont_diff_at_arcsin_iff <;>
     simpa [arccos] using (@contDiffAt_const _ _ _ _ _ _ _ _ _ _ (π / 2)).sub h
 #align real.cont_diff_at_arccos_iff Real.contDiffAt_arccos_iff
+-/
 
 end Arccos

36938f77

bump to nightly-2023-06-07-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

831e78ce

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
 
 ! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.inverse_deriv
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.SpecialFunctions.Trigonometric.Deriv
 /-!
 # derivatives of the inverse trigonometric functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Derivatives of `arcsin` and `arccos`.
 -/

f2ce6086

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -75,7 +75,7 @@ theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
   by
   rcases em (x = 1) with (rfl | h')
   ·
-    convert(hasDerivWithinAt_const _ _ (π / 2)).congr _ _ <;>
+    convert (hasDerivWithinAt_const _ _ (π / 2)).congr _ _ <;>
       simp (config := { contextual := true }) [arcsin_of_one_le]
   · exact (has_deriv_at_arcsin h h').HasDerivWithinAt
 #align real.has_deriv_within_at_arcsin_Ici Real.hasDerivWithinAt_arcsin_Ici
@@ -85,7 +85,7 @@ theorem hasDerivWithinAt_arcsin_Iic {x : ℝ} (h : x ≠ 1) :
   by
   rcases em (x = -1) with (rfl | h')
   ·
-    convert(hasDerivWithinAt_const _ _ (-(π / 2))).congr _ _ <;>
+    convert (hasDerivWithinAt_const _ _ (-(π / 2))).congr _ _ <;>
       simp (config := { contextual := true }) [arcsin_of_le_neg_one]
   · exact (has_deriv_at_arcsin h' h).HasDerivWithinAt
 #align real.has_deriv_within_at_arcsin_Iic Real.hasDerivWithinAt_arcsin_Iic
@@ -96,8 +96,8 @@ theorem differentiableWithinAt_arcsin_Ici {x : ℝ} :
   refine' ⟨_, fun h => (has_deriv_within_at_arcsin_Ici h).DifferentiableWithinAt⟩
   rintro h rfl
   have : sin ∘ arcsin =ᶠ[𝓝[≥] (-1 : ℝ)] id := by
-    filter_upwards [Icc_mem_nhdsWithin_Ici
-        ⟨le_rfl, neg_lt_self (zero_lt_one' ℝ)⟩]with x using sin_arcsin'
+    filter_upwards [Icc_mem_nhdsWithin_Ici ⟨le_rfl, neg_lt_self (zero_lt_one' ℝ)⟩] with x using
+      sin_arcsin'
   have := h.has_deriv_within_at.sin.congr_of_eventually_eq this.symm (by simp)
   simpa using (uniqueDiffOn_Ici _ _ left_mem_Ici).eq_deriv _ this (hasDerivWithinAt_id _ _)
 #align real.differentiable_within_at_arcsin_Ici Real.differentiableWithinAt_arcsin_Ici

f2ce6086

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -43,7 +43,7 @@ theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
         cont_diff_at_const.congr_of_eventually_eq this⟩
   cases' h₂.lt_or_lt with h₂ h₂
   · have : 0 < sqrt (1 - x ^ 2) := sqrt_pos.2 (by nlinarith [h₁, h₂])
-    simp only [← cos_arcsin, one_div] at this⊢
+    simp only [← cos_arcsin, one_div] at this ⊢
     exact
       ⟨sin_local_homeomorph.has_strict_deriv_at_symm ⟨h₁, h₂⟩ this.ne' (has_strict_deriv_at_sin _),
         sin_local_homeomorph.cont_diff_at_symm_deriv this.ne' ⟨h₁, h₂⟩ (has_deriv_at_sin _)
@@ -106,7 +106,7 @@ theorem differentiableWithinAt_arcsin_Iic {x : ℝ} :
     DifferentiableWithinAt ℝ arcsin (Iic x) x ↔ x ≠ 1 :=
   by
   refine' ⟨fun h => _, fun h => (has_deriv_within_at_arcsin_Iic h).DifferentiableWithinAt⟩
-  rw [← neg_neg x, ← image_neg_Ici] at h
+  rw [← neg_neg x, ← image_neg_Ici] at h 
   have := (h.comp (-x) differentiable_within_at_id.neg (maps_to_image _ _)).neg
   simpa [(· ∘ ·), differentiable_within_at_arcsin_Ici] using this
 #align real.differentiable_within_at_arcsin_Iic Real.differentiableWithinAt_arcsin_Iic
@@ -125,7 +125,7 @@ theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) :=
   by_cases h : x ≠ -1 ∧ x ≠ 1
   · exact (has_deriv_at_arcsin h.1 h.2).deriv
   · rw [deriv_zero_of_not_differentiableAt (mt differentiable_at_arcsin.1 h)]
-    simp only [not_and_or, Ne.def, Classical.not_not] at h
+    simp only [not_and_or, Ne.def, Classical.not_not] at h 
     rcases h with (rfl | rfl) <;> simp
 #align real.deriv_arcsin Real.deriv_arcsin

f2ce6086

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -20,11 +20,11 @@ Derivatives of `arcsin` and `arccos`.
 
 noncomputable section
 
-open Classical Topology Filter
+open scoped Classical Topology Filter
 
 open Set Filter
 
-open Real
+open scoped Real
 
 namespace Real

f2ce6086

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -75,7 +75,7 @@ theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
   by
   rcases em (x = 1) with (rfl | h')
   ·
-    convert (hasDerivWithinAt_const _ _ (π / 2)).congr _ _ <;>
+    convert(hasDerivWithinAt_const _ _ (π / 2)).congr _ _ <;>
       simp (config := { contextual := true }) [arcsin_of_one_le]
   · exact (has_deriv_at_arcsin h h').HasDerivWithinAt
 #align real.has_deriv_within_at_arcsin_Ici Real.hasDerivWithinAt_arcsin_Ici
@@ -85,7 +85,7 @@ theorem hasDerivWithinAt_arcsin_Iic {x : ℝ} (h : x ≠ 1) :
   by
   rcases em (x = -1) with (rfl | h')
   ·
-    convert (hasDerivWithinAt_const _ _ (-(π / 2))).congr _ _ <;>
+    convert(hasDerivWithinAt_const _ _ (-(π / 2))).congr _ _ <;>
       simp (config := { contextual := true }) [arcsin_of_le_neg_one]
   · exact (has_deriv_at_arcsin h' h).HasDerivWithinAt
 #align real.has_deriv_within_at_arcsin_Iic Real.hasDerivWithinAt_arcsin_Iic

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

feat: add notation for Real.sqrt (#12056)

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

Is far more common thatn NNReal.sqrt and Nat.sqrt
Is far more interesting to mathlib than sqrt on Float
Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

8640948c

Diff

@@ -28,7 +28,7 @@ namespace Real
 section Arcsin
 
 theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
-    HasStrictDerivAt arcsin (1 / sqrt (1 - x ^ 2)) x ∧ ContDiffAt ℝ ⊤ arcsin x := by
+    HasStrictDerivAt arcsin (1 / √(1 - x ^ 2)) x ∧ ContDiffAt ℝ ⊤ arcsin x := by
   cases' h₁.lt_or_lt with h₁ h₁
   · have : 1 - x ^ 2 < 0 := by nlinarith [h₁]
     rw [sqrt_eq_zero'.2 this.le, div_zero]
@@ -37,7 +37,7 @@ theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
     exact ⟨(hasStrictDerivAt_const _ _).congr_of_eventuallyEq this.symm,
       contDiffAt_const.congr_of_eventuallyEq this⟩
   cases' h₂.lt_or_lt with h₂ h₂
-  · have : 0 < sqrt (1 - x ^ 2) := sqrt_pos.2 (by nlinarith [h₁, h₂])
+  · have : 0 < √(1 - x ^ 2) := sqrt_pos.2 (by nlinarith [h₁, h₂])
     simp only [← cos_arcsin, one_div] at this ⊢
     exact ⟨sinPartialHomeomorph.hasStrictDerivAt_symm ⟨h₁, h₂⟩ this.ne' (hasStrictDerivAt_sin _),
       sinPartialHomeomorph.contDiffAt_symm_deriv this.ne' ⟨h₁, h₂⟩ (hasDerivAt_sin _)
@@ -50,12 +50,12 @@ theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
 #align real.deriv_arcsin_aux Real.deriv_arcsin_aux
 
 theorem hasStrictDerivAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
-    HasStrictDerivAt arcsin (1 / sqrt (1 - x ^ 2)) x :=
+    HasStrictDerivAt arcsin (1 / √(1 - x ^ 2)) x :=
   (deriv_arcsin_aux h₁ h₂).1
 #align real.has_strict_deriv_at_arcsin Real.hasStrictDerivAt_arcsin
 
 theorem hasDerivAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
-    HasDerivAt arcsin (1 / sqrt (1 - x ^ 2)) x :=
+    HasDerivAt arcsin (1 / √(1 - x ^ 2)) x :=
   (hasStrictDerivAt_arcsin h₁ h₂).hasDerivAt
 #align real.has_deriv_at_arcsin Real.hasDerivAt_arcsin
 
@@ -64,7 +64,7 @@ theorem contDiffAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) {n : ℕ
 #align real.cont_diff_at_arcsin Real.contDiffAt_arcsin
 
 theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
-    HasDerivWithinAt arcsin (1 / sqrt (1 - x ^ 2)) (Ici x) x := by
+    HasDerivWithinAt arcsin (1 / √(1 - x ^ 2)) (Ici x) x := by
   rcases eq_or_ne x 1 with (rfl | h')
   · convert (hasDerivWithinAt_const (1 : ℝ) _ (π / 2)).congr _ _ <;>
       simp (config := { contextual := true }) [arcsin_of_one_le]
@@ -72,7 +72,7 @@ theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
 #align real.has_deriv_within_at_arcsin_Ici Real.hasDerivWithinAt_arcsin_Ici
 
 theorem hasDerivWithinAt_arcsin_Iic {x : ℝ} (h : x ≠ 1) :
-    HasDerivWithinAt arcsin (1 / sqrt (1 - x ^ 2)) (Iic x) x := by
+    HasDerivWithinAt arcsin (1 / √(1 - x ^ 2)) (Iic x) x := by
   rcases em (x = -1) with (rfl | h')
   · convert (hasDerivWithinAt_const (-1 : ℝ) _ (-(π / 2))).congr _ _ <;>
       simp (config := { contextual := true }) [arcsin_of_le_neg_one]
@@ -105,7 +105,7 @@ theorem differentiableAt_arcsin {x : ℝ} : DifferentiableAt ℝ arcsin x ↔ x
 #align real.differentiable_at_arcsin Real.differentiableAt_arcsin
 
 @[simp]
-theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) := by
+theorem deriv_arcsin : deriv arcsin = fun x => 1 / √(1 - x ^ 2) := by
   funext x
   by_cases h : x ≠ -1 ∧ x ≠ 1
   · exact (hasDerivAt_arcsin h.1 h.2).deriv
@@ -135,12 +135,12 @@ end Arcsin
 section Arccos
 
 theorem hasStrictDerivAt_arccos {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
-    HasStrictDerivAt arccos (-(1 / sqrt (1 - x ^ 2))) x :=
+    HasStrictDerivAt arccos (-(1 / √(1 - x ^ 2))) x :=
   (hasStrictDerivAt_arcsin h₁ h₂).const_sub (π / 2)
 #align real.has_strict_deriv_at_arccos Real.hasStrictDerivAt_arccos
 
 theorem hasDerivAt_arccos {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
-    HasDerivAt arccos (-(1 / sqrt (1 - x ^ 2))) x :=
+    HasDerivAt arccos (-(1 / √(1 - x ^ 2))) x :=
   (hasDerivAt_arcsin h₁ h₂).const_sub (π / 2)
 #align real.has_deriv_at_arccos Real.hasDerivAt_arccos
 
@@ -149,12 +149,12 @@ theorem contDiffAt_arccos {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) {n : ℕ
 #align real.cont_diff_at_arccos Real.contDiffAt_arccos
 
 theorem hasDerivWithinAt_arccos_Ici {x : ℝ} (h : x ≠ -1) :
-    HasDerivWithinAt arccos (-(1 / sqrt (1 - x ^ 2))) (Ici x) x :=
+    HasDerivWithinAt arccos (-(1 / √(1 - x ^ 2))) (Ici x) x :=
   (hasDerivWithinAt_arcsin_Ici h).const_sub _
 #align real.has_deriv_within_at_arccos_Ici Real.hasDerivWithinAt_arccos_Ici
 
 theorem hasDerivWithinAt_arccos_Iic {x : ℝ} (h : x ≠ 1) :
-    HasDerivWithinAt arccos (-(1 / sqrt (1 - x ^ 2))) (Iic x) x :=
+    HasDerivWithinAt arccos (-(1 / √(1 - x ^ 2))) (Iic x) x :=
   (hasDerivWithinAt_arcsin_Iic h).const_sub _
 #align real.has_deriv_within_at_arccos_Iic Real.hasDerivWithinAt_arccos_Iic
 
@@ -173,7 +173,7 @@ theorem differentiableAt_arccos {x : ℝ} : DifferentiableAt ℝ arccos x ↔ x
 #align real.differentiable_at_arccos Real.differentiableAt_arccos
 
 @[simp]
-theorem deriv_arccos : deriv arccos = fun x => -(1 / sqrt (1 - x ^ 2)) :=
+theorem deriv_arccos : deriv arccos = fun x => -(1 / √(1 - x ^ 2)) :=
   funext fun x => (deriv_const_sub _).trans <| by simp only [deriv_arcsin]
 #align real.deriv_arccos Real.deriv_arccos

f2ce6086

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -110,7 +110,7 @@ theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) := by
   by_cases h : x ≠ -1 ∧ x ≠ 1
   · exact (hasDerivAt_arcsin h.1 h.2).deriv
   · rw [deriv_zero_of_not_differentiableAt (mt differentiableAt_arcsin.1 h)]
-    simp only [not_and_or, Ne.def, Classical.not_not] at h
+    simp only [not_and_or, Ne, Classical.not_not] at h
     rcases h with (rfl | rfl) <;> simp
 #align real.deriv_arcsin Real.deriv_arcsin

f2ce6086

chore: rename LocalHomeomorph to PartialHomeomorph (#8982)

LocalHomeomorph evokes a "local homeomorphism": this is not what this means. Instead, this is a homeomorphism on an open set of the domain (extended to the whole space, by the junk value pattern). Hence, partial homeomorphism is more appropriate, and avoids confusion with IsLocallyHomeomorph.

A future PR will rename LocalEquiv to PartialEquiv.

Zulip discussion

bbc6e56d

Diff

@@ -39,8 +39,8 @@ theorem deriv_arcsin_aux {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) :
   cases' h₂.lt_or_lt with h₂ h₂
   · have : 0 < sqrt (1 - x ^ 2) := sqrt_pos.2 (by nlinarith [h₁, h₂])
     simp only [← cos_arcsin, one_div] at this ⊢
-    exact ⟨sinLocalHomeomorph.hasStrictDerivAt_symm ⟨h₁, h₂⟩ this.ne' (hasStrictDerivAt_sin _),
-      sinLocalHomeomorph.contDiffAt_symm_deriv this.ne' ⟨h₁, h₂⟩ (hasDerivAt_sin _)
+    exact ⟨sinPartialHomeomorph.hasStrictDerivAt_symm ⟨h₁, h₂⟩ this.ne' (hasStrictDerivAt_sin _),
+      sinPartialHomeomorph.contDiffAt_symm_deriv this.ne' ⟨h₁, h₂⟩ (hasDerivAt_sin _)
         contDiff_sin.contDiffAt⟩
   · have : 1 - x ^ 2 < 0 := by nlinarith [h₂]
     rw [sqrt_eq_zero'.2 this.le, div_zero]

f2ce6086

refactor: replace some [@foo](https://github.com/foo) _ _ _ _ _ ... by named arguments (#8702)

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

df634f2a

Diff

@@ -188,7 +188,7 @@ theorem contDiffOn_arccos {n : ℕ∞} : ContDiffOn ℝ n arccos {-1, 1}ᶜ :=
 theorem contDiffAt_arccos_iff {x : ℝ} {n : ℕ∞} :
     ContDiffAt ℝ n arccos x ↔ n = 0 ∨ x ≠ -1 ∧ x ≠ 1 := by
   refine' Iff.trans ⟨fun h => _, fun h => _⟩ contDiffAt_arcsin_iff <;>
-    simpa [arccos] using (@contDiffAt_const _ _ _ _ _ _ _ _ _ _ (π / 2)).sub h
+    simpa [arccos] using (contDiffAt_const (c := π / 2)).sub h
 #align real.cont_diff_at_arccos_iff Real.contDiffAt_arccos_iff
 
 end Arccos

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.inverse_deriv
-! 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.Inverse
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
 
+#align_import analysis.special_functions.trigonometric.inverse_deriv from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # derivatives of the inverse trigonometric functions

f2ce6086

fix: change compl precedence (#5586)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

4d4f0f25

Diff

@@ -96,7 +96,7 @@ theorem differentiableWithinAt_arcsin_Ici {x : ℝ} :
 theorem differentiableWithinAt_arcsin_Iic {x : ℝ} :
     DifferentiableWithinAt ℝ arcsin (Iic x) x ↔ x ≠ 1 := by
   refine' ⟨fun h => _, fun h => (hasDerivWithinAt_arcsin_Iic h).differentiableWithinAt⟩
-  rw [← neg_neg x, ← image_neg_Ici] at h 
+  rw [← neg_neg x, ← image_neg_Ici] at h
   have := (h.comp (-x) differentiableWithinAt_id.neg (mapsTo_image _ _)).neg
   simpa [(· ∘ ·), differentiableWithinAt_arcsin_Ici] using this
 #align real.differentiable_within_at_arcsin_Iic Real.differentiableWithinAt_arcsin_Iic
@@ -113,16 +113,16 @@ theorem deriv_arcsin : deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2) := by
   by_cases h : x ≠ -1 ∧ x ≠ 1
   · exact (hasDerivAt_arcsin h.1 h.2).deriv
   · rw [deriv_zero_of_not_differentiableAt (mt differentiableAt_arcsin.1 h)]
-    simp only [not_and_or, Ne.def, Classical.not_not] at h 
+    simp only [not_and_or, Ne.def, Classical.not_not] at h
     rcases h with (rfl | rfl) <;> simp
 #align real.deriv_arcsin Real.deriv_arcsin
 
-theorem differentiableOn_arcsin : DifferentiableOn ℝ arcsin ({-1, 1}ᶜ) := fun _x hx =>
+theorem differentiableOn_arcsin : DifferentiableOn ℝ arcsin {-1, 1}ᶜ := fun _x hx =>
   (differentiableAt_arcsin.2
       ⟨fun h => hx (Or.inl h), fun h => hx (Or.inr h)⟩).differentiableWithinAt
 #align real.differentiable_on_arcsin Real.differentiableOn_arcsin
 
-theorem contDiffOn_arcsin {n : ℕ∞} : ContDiffOn ℝ n arcsin ({-1, 1}ᶜ) := fun _x hx =>
+theorem contDiffOn_arcsin {n : ℕ∞} : ContDiffOn ℝ n arcsin {-1, 1}ᶜ := fun _x hx =>
   (contDiffAt_arcsin (mt Or.inl hx) (mt Or.inr hx)).contDiffWithinAt
 #align real.cont_diff_on_arcsin Real.contDiffOn_arcsin
 
@@ -180,11 +180,11 @@ theorem deriv_arccos : deriv arccos = fun x => -(1 / sqrt (1 - x ^ 2)) :=
   funext fun x => (deriv_const_sub _).trans <| by simp only [deriv_arcsin]
 #align real.deriv_arccos Real.deriv_arccos
 
-theorem differentiableOn_arccos : DifferentiableOn ℝ arccos ({-1, 1}ᶜ) :=
+theorem differentiableOn_arccos : DifferentiableOn ℝ arccos {-1, 1}ᶜ :=
   differentiableOn_arcsin.const_sub _
 #align real.differentiable_on_arccos Real.differentiableOn_arccos
 
-theorem contDiffOn_arccos {n : ℕ∞} : ContDiffOn ℝ n arccos ({-1, 1}ᶜ) :=
+theorem contDiffOn_arccos {n : ℕ∞} : ContDiffOn ℝ n arccos {-1, 1}ᶜ :=
   contDiffOn_const.sub contDiffOn_arcsin
 #align real.cont_diff_on_arccos Real.contDiffOn_arccos

f2ce6086

feat: port Analysis.SpecialFunctions.Trigonometric.InverseDeriv (#4676)

ddef6f41

`analysis.special_functions.trigonometric.inverse_deriv` ⟷ `Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 897

analysis.special_functions.trigonometric.inverse_deriv ⟷ Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 897

`analysis.special_functions.trigonometric.inverse_deriv` ⟷ `Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv`