analysis.calculus.deriv.inverse ⟷ Mathlib.Analysis.Calculus.Deriv.Inverse

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
 import Analysis.Calculus.Deriv.Comp
-import Analysis.Calculus.Fderiv.Equiv
+import Analysis.Calculus.FDeriv.Equiv
 
 #align_import analysis.calculus.deriv.inverse from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 

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

@@ -79,18 +79,18 @@ theorem HasStrictDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 
 #align has_strict_deriv_at.of_local_left_inverse HasStrictDerivAt.of_local_left_inverse
 -/
 
-#print LocalHomeomorph.hasStrictDerivAt_symm /-
+#print PartialHomeomorph.hasStrictDerivAt_symm /-
 /-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
 nonzero derivative `f'` at `f.symm a` in the strict sense, then `f.symm` has the derivative `f'⁻¹`
 at `a` in the strict sense.
 
 This is one of the easy parts of the inverse function theorem: it assumes that we already have
 an inverse function. -/
-theorem LocalHomeomorph.hasStrictDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a f' : 𝕜}
+theorem PartialHomeomorph.hasStrictDerivAt_symm (f : PartialHomeomorph 𝕜 𝕜) {a f' : 𝕜}
     (ha : a ∈ f.target) (hf' : f' ≠ 0) (htff' : HasStrictDerivAt f f' (f.symm a)) :
     HasStrictDerivAt f.symm f'⁻¹ a :=
   htff'.of_local_left_inverse (f.symm.ContinuousAt ha) hf' (f.eventually_right_inverse ha)
-#align local_homeomorph.has_strict_deriv_at_symm LocalHomeomorph.hasStrictDerivAt_symm
+#align local_homeomorph.has_strict_deriv_at_symm PartialHomeomorph.hasStrictDerivAt_symm
 -/
 
 #print HasDerivAt.of_local_left_inverse /-
@@ -106,16 +106,16 @@ theorem HasDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 𝕜} (hg
 #align has_deriv_at.of_local_left_inverse HasDerivAt.of_local_left_inverse
 -/
 
-#print LocalHomeomorph.hasDerivAt_symm /-
+#print PartialHomeomorph.hasDerivAt_symm /-
 /-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has an
 nonzero derivative `f'` at `f.symm a`, then `f.symm` has the derivative `f'⁻¹` at `a`.
 
 This is one of the easy parts of the inverse function theorem: it assumes that we already have
 an inverse function. -/
-theorem LocalHomeomorph.hasDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a f' : 𝕜} (ha : a ∈ f.target)
+theorem PartialHomeomorph.hasDerivAt_symm (f : PartialHomeomorph 𝕜 𝕜) {a f' : 𝕜} (ha : a ∈ f.target)
     (hf' : f' ≠ 0) (htff' : HasDerivAt f f' (f.symm a)) : HasDerivAt f.symm f'⁻¹ a :=
   htff'.of_local_left_inverse (f.symm.ContinuousAt ha) hf' (f.eventually_right_inverse ha)
-#align local_homeomorph.has_deriv_at_symm LocalHomeomorph.hasDerivAt_symm
+#align local_homeomorph.has_deriv_at_symm PartialHomeomorph.hasDerivAt_symm
 -/
 
 #print HasDerivAt.eventually_ne /-

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Analysis.Calculus.Deriv.Comp
-import Mathbin.Analysis.Calculus.Fderiv.Equiv
+import Analysis.Calculus.Deriv.Comp
+import Analysis.Calculus.Fderiv.Equiv
 
 #align_import analysis.calculus.deriv.inverse from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.deriv.inverse
-! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Deriv.Comp
 import Mathbin.Analysis.Calculus.Fderiv.Equiv
 
+#align_import analysis.calculus.deriv.inverse from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
 /-!
 # Inverse function theorem - the easy half
 

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

@@ -52,18 +52,23 @@ variable {s t : Set 𝕜}
 
 variable {L L₁ L₂ : Filter 𝕜}
 
+#print HasStrictDerivAt.hasStrictFDerivAt_equiv /-
 theorem HasStrictDerivAt.hasStrictFDerivAt_equiv {f : 𝕜 → 𝕜} {f' x : 𝕜}
     (hf : HasStrictDerivAt f f' x) (hf' : f' ≠ 0) :
     HasStrictFDerivAt f (ContinuousLinearEquiv.unitsEquivAut 𝕜 (Units.mk0 f' hf') : 𝕜 →L[𝕜] 𝕜) x :=
   hf
 #align has_strict_deriv_at.has_strict_fderiv_at_equiv HasStrictDerivAt.hasStrictFDerivAt_equiv
+-/
 
+#print HasDerivAt.hasFDerivAt_equiv /-
 theorem HasDerivAt.hasFDerivAt_equiv {f : 𝕜 → 𝕜} {f' x : 𝕜} (hf : HasDerivAt f f' x)
     (hf' : f' ≠ 0) :
     HasFDerivAt f (ContinuousLinearEquiv.unitsEquivAut 𝕜 (Units.mk0 f' hf') : 𝕜 →L[𝕜] 𝕜) x :=
   hf
 #align has_deriv_at.has_fderiv_at_equiv HasDerivAt.hasFDerivAt_equiv
+-/
 
+#print HasStrictDerivAt.of_local_left_inverse /-
 /-- If `f (g y) = y` for `y` in some neighborhood of `a`, `g` is continuous at `a`, and `f` has an
 invertible derivative `f'` at `g a` in the strict sense, then `g` has the derivative `f'⁻¹` at `a`
 in the strict sense.
@@ -75,7 +80,9 @@ theorem HasStrictDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 
     HasStrictDerivAt g f'⁻¹ a :=
   (hf.hasStrictFDerivAt_equiv hf').of_local_left_inverse hg hfg
 #align has_strict_deriv_at.of_local_left_inverse HasStrictDerivAt.of_local_left_inverse
+-/
 
+#print LocalHomeomorph.hasStrictDerivAt_symm /-
 /-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
 nonzero derivative `f'` at `f.symm a` in the strict sense, then `f.symm` has the derivative `f'⁻¹`
 at `a` in the strict sense.
@@ -87,7 +94,9 @@ theorem LocalHomeomorph.hasStrictDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a
     HasStrictDerivAt f.symm f'⁻¹ a :=
   htff'.of_local_left_inverse (f.symm.ContinuousAt ha) hf' (f.eventually_right_inverse ha)
 #align local_homeomorph.has_strict_deriv_at_symm LocalHomeomorph.hasStrictDerivAt_symm
+-/
 
+#print HasDerivAt.of_local_left_inverse /-
 /-- If `f (g y) = y` for `y` in some neighborhood of `a`, `g` is continuous at `a`, and `f` has an
 invertible derivative `f'` at `g a`, then `g` has the derivative `f'⁻¹` at `a`.
 
@@ -98,7 +107,9 @@ theorem HasDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 𝕜} (hg
     HasDerivAt g f'⁻¹ a :=
   (hf.hasFDerivAt_equiv hf').of_local_left_inverse hg hfg
 #align has_deriv_at.of_local_left_inverse HasDerivAt.of_local_left_inverse
+-/
 
+#print LocalHomeomorph.hasDerivAt_symm /-
 /-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has an
 nonzero derivative `f'` at `f.symm a`, then `f.symm` has the derivative `f'⁻¹` at `a`.
 
@@ -108,19 +119,25 @@ theorem LocalHomeomorph.hasDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a f' :
     (hf' : f' ≠ 0) (htff' : HasDerivAt f f' (f.symm a)) : HasDerivAt f.symm f'⁻¹ a :=
   htff'.of_local_left_inverse (f.symm.ContinuousAt ha) hf' (f.eventually_right_inverse ha)
 #align local_homeomorph.has_deriv_at_symm LocalHomeomorph.hasDerivAt_symm
+-/
 
+#print HasDerivAt.eventually_ne /-
 theorem HasDerivAt.eventually_ne (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :
     ∀ᶠ z in 𝓝[≠] x, f z ≠ f x :=
   (hasDerivAt_iff_hasFDerivAt.1 h).eventually_ne
     ⟨‖f'‖⁻¹, fun z => by field_simp [norm_smul, mt norm_eq_zero.1 hf']⟩
 #align has_deriv_at.eventually_ne HasDerivAt.eventually_ne
+-/
 
+#print HasDerivAt.tendsto_punctured_nhds /-
 theorem HasDerivAt.tendsto_punctured_nhds (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :
     Tendsto f (𝓝[≠] x) (𝓝[≠] f x) :=
   tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within _ h.ContinuousAt.ContinuousWithinAt
     (h.eventually_ne hf')
 #align has_deriv_at.tendsto_punctured_nhds HasDerivAt.tendsto_punctured_nhds
+-/
 
+#print not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero /-
 theorem not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero {f g : 𝕜 → 𝕜} {a : 𝕜}
     {s t : Set 𝕜} (ha : a ∈ s) (hsu : UniqueDiffWithinAt 𝕜 s a) (hf : HasDerivWithinAt f 0 t (g a))
     (hst : MapsTo g s t) (hfg : f ∘ g =ᶠ[𝓝[s] a] id) : ¬DifferentiableWithinAt 𝕜 g s a :=
@@ -129,7 +146,9 @@ theorem not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero {
   have := (hf.comp a hg.has_deriv_within_at hst).congr_of_eventuallyEq_of_mem hfg.symm ha
   simpa using hsu.eq_deriv _ this (hasDerivWithinAt_id _ _)
 #align not_differentiable_within_at_of_local_left_inverse_has_deriv_within_at_zero not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero
+-/
 
+#print not_differentiableAt_of_local_left_inverse_hasDerivAt_zero /-
 theorem not_differentiableAt_of_local_left_inverse_hasDerivAt_zero {f g : 𝕜 → 𝕜} {a : 𝕜}
     (hf : HasDerivAt f 0 (g a)) (hfg : f ∘ g =ᶠ[𝓝 a] id) : ¬DifferentiableAt 𝕜 g a :=
   by
@@ -137,4 +156,5 @@ theorem not_differentiableAt_of_local_left_inverse_hasDerivAt_zero {f g : 𝕜 
   have := (hf.comp a hg.has_deriv_at).congr_of_eventuallyEq hfg.symm
   simpa using this.unique (hasDerivAt_id a)
 #align not_differentiable_at_of_local_left_inverse_has_deriv_at_zero not_differentiableAt_of_local_left_inverse_hasDerivAt_zero
+-/
 

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

@@ -112,7 +112,7 @@ theorem LocalHomeomorph.hasDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a f' :
 theorem HasDerivAt.eventually_ne (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :
     ∀ᶠ z in 𝓝[≠] x, f z ≠ f x :=
   (hasDerivAt_iff_hasFDerivAt.1 h).eventually_ne
-    ⟨‖f'‖⁻¹, fun z => by field_simp [norm_smul, mt norm_eq_zero.1 hf'] ⟩
+    ⟨‖f'‖⁻¹, fun z => by field_simp [norm_smul, mt norm_eq_zero.1 hf']⟩
 #align has_deriv_at.eventually_ne HasDerivAt.eventually_ne
 
 theorem HasDerivAt.tendsto_punctured_nhds (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.calculus.deriv.inverse
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
+! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
 ! 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.Calculus.Fderiv.Equiv
 /-!
 # Inverse function theorem - the easy half
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that `g' (f x) = (f' x)⁻¹` provided that `f` is strictly differentiable at
 `x`, `f' x ≠ 0`, and `g` is a local left inverse of `f` that is continuous at `f x`. This is the
 easy half of the inverse function theorem: the harder half states that `g` exists.

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

@@ -29,7 +29,7 @@ derivative, inverse function
 
 universe u v w
 
-open Classical Topology BigOperators Filter ENNReal
+open scoped Classical Topology BigOperators Filter ENNReal
 
 open Filter Asymptotics Set
 

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

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -32,19 +32,12 @@ open Topology BigOperators Filter ENNReal
 open Filter Asymptotics Set
 
 variable {𝕜 : Type u} [NontriviallyNormedField 𝕜]
-
 variable {F : Type v} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-
 variable {E : Type w} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
-
 variable {f f₀ f₁ g : 𝕜 → F}
-
 variable {f' f₀' f₁' g' : F}
-
 variable {x : 𝕜}
-
 variable {s t : Set 𝕜}
-
 variable {L L₁ L₂ : Filter 𝕜}
 
 theorem HasStrictDerivAt.hasStrictFDerivAt_equiv {f : 𝕜 → 𝕜} {f' x : 𝕜}

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -26,7 +26,8 @@ derivative, inverse function
 
 universe u v w
 
-open Classical Topology BigOperators Filter ENNReal
+open scoped Classical
+open Topology BigOperators Filter ENNReal
 
 open Filter Asymptotics Set
 

This cleans up instances of

⟨ foo, bar⟩

and

⟨foo, bar ⟩

where spaces a on the inside one side, but not on the other side. Fixing this by removing the extra space.

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -106,7 +106,7 @@ theorem PartialHomeomorph.hasDerivAt_symm (f : PartialHomeomorph 𝕜 𝕜) {a f
 theorem HasDerivAt.eventually_ne (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :
     ∀ᶠ z in 𝓝[≠] x, f z ≠ f x :=
   (hasDerivAt_iff_hasFDerivAt.1 h).eventually_ne
-    ⟨‖f'‖⁻¹, fun z => by field_simp [norm_smul, mt norm_eq_zero.1 hf'] ⟩
+    ⟨‖f'‖⁻¹, fun z => by field_simp [norm_smul, mt norm_eq_zero.1 hf']⟩
 #align has_deriv_at.eventually_ne HasDerivAt.eventually_ne
 
 theorem HasDerivAt.tendsto_punctured_nhds (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :

Almost all of them should speak about partial homeomorphisms instead. In two cases, I decided removing the "local" was clearer than adding "partial".

Follow-up to #8982; complements #9238.

@@ -70,7 +70,7 @@ theorem HasStrictDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 
   (hf.hasStrictFDerivAt_equiv hf').of_local_left_inverse hg hfg
 #align has_strict_deriv_at.of_local_left_inverse HasStrictDerivAt.of_local_left_inverse
 
-/-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
+/-- If `f` is a partial homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
 nonzero derivative `f'` at `f.symm a` in the strict sense, then `f.symm` has the derivative `f'⁻¹`
 at `a` in the strict sense.
 
@@ -93,7 +93,7 @@ theorem HasDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 𝕜} (hg
   (hf.hasFDerivAt_equiv hf').of_local_left_inverse hg hfg
 #align has_deriv_at.of_local_left_inverse HasDerivAt.of_local_left_inverse
 
-/-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
+/-- If `f` is a partial homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
 nonzero derivative `f'` at `f.symm a`, then `f.symm` has the derivative `f'⁻¹` at `a`.
 
 This is one of the easy parts of the inverse function theorem: it assumes that we already have

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

@@ -76,11 +76,11 @@ at `a` in the strict sense.
 
 This is one of the easy parts of the inverse function theorem: it assumes that we already have
 an inverse function. -/
-theorem LocalHomeomorph.hasStrictDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a f' : 𝕜}
+theorem PartialHomeomorph.hasStrictDerivAt_symm (f : PartialHomeomorph 𝕜 𝕜) {a f' : 𝕜}
     (ha : a ∈ f.target) (hf' : f' ≠ 0) (htff' : HasStrictDerivAt f f' (f.symm a)) :
     HasStrictDerivAt f.symm f'⁻¹ a :=
   htff'.of_local_left_inverse (f.symm.continuousAt ha) hf' (f.eventually_right_inverse ha)
-#align local_homeomorph.has_strict_deriv_at_symm LocalHomeomorph.hasStrictDerivAt_symm
+#align local_homeomorph.has_strict_deriv_at_symm PartialHomeomorph.hasStrictDerivAt_symm
 
 /-- If `f (g y) = y` for `y` in some neighborhood of `a`, `g` is continuous at `a`, and `f` has an
 invertible derivative `f'` at `g a`, then `g` has the derivative `f'⁻¹` at `a`.
@@ -98,10 +98,10 @@ nonzero derivative `f'` at `f.symm a`, then `f.symm` has the derivative `f'⁻¹
 
 This is one of the easy parts of the inverse function theorem: it assumes that we already have
 an inverse function. -/
-theorem LocalHomeomorph.hasDerivAt_symm (f : LocalHomeomorph 𝕜 𝕜) {a f' : 𝕜} (ha : a ∈ f.target)
+theorem PartialHomeomorph.hasDerivAt_symm (f : PartialHomeomorph 𝕜 𝕜) {a f' : 𝕜} (ha : a ∈ f.target)
     (hf' : f' ≠ 0) (htff' : HasDerivAt f f' (f.symm a)) : HasDerivAt f.symm f'⁻¹ a :=
   htff'.of_local_left_inverse (f.symm.continuousAt ha) hf' (f.eventually_right_inverse ha)
-#align local_homeomorph.has_deriv_at_symm LocalHomeomorph.hasDerivAt_symm
+#align local_homeomorph.has_deriv_at_symm PartialHomeomorph.hasDerivAt_symm
 
 theorem HasDerivAt.eventually_ne (h : HasDerivAt f f' x) (hf' : f' ≠ 0) :
     ∀ᶠ z in 𝓝[≠] x, f z ≠ f x :=

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.deriv.inverse
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Calculus.Deriv.Comp
 import Mathlib.Analysis.Calculus.FDeriv.Equiv
 
+#align_import analysis.calculus.deriv.inverse from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-!
 # Inverse function theorem - the easy half
 

All of these are doc fixes

@@ -96,7 +96,7 @@ theorem HasDerivAt.of_local_left_inverse {f g : 𝕜 → 𝕜} {f' a : 𝕜} (hg
   (hf.hasFDerivAt_equiv hf').of_local_left_inverse hg hfg
 #align has_deriv_at.of_local_left_inverse HasDerivAt.of_local_left_inverse
 
-/-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has an
+/-- If `f` is a local homeomorphism defined on a neighbourhood of `f.symm a`, and `f` has a
 nonzero derivative `f'` at `f.symm a`, then `f.symm` has the derivative `f'⁻¹` at `a`.
 
 This is one of the easy parts of the inverse function theorem: it assumes that we already have
@@ -132,4 +132,3 @@ theorem not_differentiableAt_of_local_left_inverse_hasDerivAt_zero {f g : 𝕜 
   have := (hf.comp a hg.hasDerivAt).congr_of_eventuallyEq hfg.symm
   simpa using this.unique (hasDerivAt_id a)
 #align not_differentiable_at_of_local_left_inverse_has_deriv_at_zero not_differentiableAt_of_local_left_inverse_hasDerivAt_zero
-