analysis.calculus.deriv.comp ⟷ Mathlib.Analysis.Calculus.Deriv.Comp

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

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao
 -/
 import Analysis.Calculus.Deriv.Basic
-import Analysis.Calculus.Fderiv.Comp
-import Analysis.Calculus.Fderiv.RestrictScalars
+import Analysis.Calculus.FDeriv.Comp
+import Analysis.Calculus.FDeriv.RestrictScalars
 
 #align_import analysis.calculus.deriv.comp from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 

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

@@ -152,7 +152,7 @@ theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[
     (hh : HasStrictDerivAt h₂ h₂' (f x)) (hf : HasStrictFDerivAt f f' x) :
     HasStrictFDerivAt (h₂ ∘ f) (h₂' • f') x :=
   by
-  rw [HasStrictDerivAt] at hh 
+  rw [HasStrictDerivAt] at hh
   convert (hh.restrict_scalars 𝕜).comp x hf
   ext x
   simp [mul_comm]
@@ -240,7 +240,7 @@ protected theorem HasDerivAtFilter.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf :
     (hL : Tendsto f L L) (hx : f x = x) (n : ℕ) : HasDerivAtFilter (f^[n]) (f' ^ n) x L :=
   by
   have := hf.iterate hL hx n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_deriv_at_filter.iterate HasDerivAtFilter.iterate
 -/
 
@@ -249,7 +249,7 @@ protected theorem HasDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDe
     (n : ℕ) : HasDerivAt (f^[n]) (f' ^ n) x :=
   by
   have := HasFDerivAt.iterate hf hx n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_deriv_at.iterate HasDerivAt.iterate
 -/
 
@@ -258,7 +258,7 @@ protected theorem HasDerivWithinAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf :
     (hx : f x = x) (hs : MapsTo f s s) (n : ℕ) : HasDerivWithinAt (f^[n]) (f' ^ n) s x :=
   by
   have := HasFDerivWithinAt.iterate hf hx hs n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_deriv_within_at.iterate HasDerivWithinAt.iterate
 -/
 
@@ -267,7 +267,7 @@ protected theorem HasStrictDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf :
     (hx : f x = x) (n : ℕ) : HasStrictDerivAt (f^[n]) (f' ^ n) x :=
   by
   have := hf.iterate hx n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_strict_deriv_at.iterate HasStrictDerivAt.iterate
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2019 Gabriel Ebner. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao
 -/
-import Mathbin.Analysis.Calculus.Deriv.Basic
-import Mathbin.Analysis.Calculus.Fderiv.Comp
-import Mathbin.Analysis.Calculus.Fderiv.RestrictScalars
+import Analysis.Calculus.Deriv.Basic
+import Analysis.Calculus.Fderiv.Comp
+import Analysis.Calculus.Fderiv.RestrictScalars
 
 #align_import analysis.calculus.deriv.comp from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Gabriel Ebner. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao
-
-! This file was ported from Lean 3 source module analysis.calculus.deriv.comp
-! 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.Basic
 import Mathbin.Analysis.Calculus.Fderiv.Comp
 import Mathbin.Analysis.Calculus.Fderiv.RestrictScalars
 
+#align_import analysis.calculus.deriv.comp from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
 /-!
 # One-dimensional derivatives of compositions of functions
 

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

@@ -79,59 +79,78 @@ variable {𝕜' : Type _} [NontriviallyNormedField 𝕜'] [NormedAlgebra 𝕜 
   [IsScalarTower 𝕜 𝕜' F] {s' t' : Set 𝕜'} {h : 𝕜 → 𝕜'} {h₁ : 𝕜 → 𝕜} {h₂ : 𝕜' → 𝕜'} {h' h₂' : 𝕜'}
   {h₁' : 𝕜} {g₁ : 𝕜' → F} {g₁' : F} {L' : Filter 𝕜'} (x)
 
+#print HasDerivAtFilter.scomp /-
 theorem HasDerivAtFilter.scomp (hg : HasDerivAtFilter g₁ g₁' (h x) L')
     (hh : HasDerivAtFilter h h' x L) (hL : Tendsto h L L') :
     HasDerivAtFilter (g₁ ∘ h) (h' • g₁') x L := by
   simpa using ((hg.restrict_scalars 𝕜).comp x hh hL).HasDerivAtFilter
 #align has_deriv_at_filter.scomp HasDerivAtFilter.scomp
+-/
 
+#print HasDerivWithinAt.scomp_hasDerivAt /-
 theorem HasDerivWithinAt.scomp_hasDerivAt (hg : HasDerivWithinAt g₁ g₁' s' (h x))
     (hh : HasDerivAt h h' x) (hs : ∀ x, h x ∈ s') : HasDerivAt (g₁ ∘ h) (h' • g₁') x :=
   hg.scomp x hh <| tendsto_inf.2 ⟨hh.ContinuousAt, tendsto_principal.2 <| eventually_of_forall hs⟩
 #align has_deriv_within_at.scomp_has_deriv_at HasDerivWithinAt.scomp_hasDerivAt
+-/
 
+#print HasDerivWithinAt.scomp /-
 theorem HasDerivWithinAt.scomp (hg : HasDerivWithinAt g₁ g₁' t' (h x))
     (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s t') :
     HasDerivWithinAt (g₁ ∘ h) (h' • g₁') s x :=
   hg.scomp x hh <| hh.ContinuousWithinAt.tendsto_nhdsWithin hst
 #align has_deriv_within_at.scomp HasDerivWithinAt.scomp
+-/
 
+#print HasDerivAt.scomp /-
 /-- The chain rule. -/
 theorem HasDerivAt.scomp (hg : HasDerivAt g₁ g₁' (h x)) (hh : HasDerivAt h h' x) :
     HasDerivAt (g₁ ∘ h) (h' • g₁') x :=
   hg.scomp x hh hh.ContinuousAt
 #align has_deriv_at.scomp HasDerivAt.scomp
+-/
 
+#print HasStrictDerivAt.scomp /-
 theorem HasStrictDerivAt.scomp (hg : HasStrictDerivAt g₁ g₁' (h x)) (hh : HasStrictDerivAt h h' x) :
     HasStrictDerivAt (g₁ ∘ h) (h' • g₁') x := by
   simpa using ((hg.restrict_scalars 𝕜).comp x hh).HasStrictDerivAt
 #align has_strict_deriv_at.scomp HasStrictDerivAt.scomp
+-/
 
+#print HasDerivAt.scomp_hasDerivWithinAt /-
 theorem HasDerivAt.scomp_hasDerivWithinAt (hg : HasDerivAt g₁ g₁' (h x))
     (hh : HasDerivWithinAt h h' s x) : HasDerivWithinAt (g₁ ∘ h) (h' • g₁') s x :=
   HasDerivWithinAt.scomp x hg.HasDerivWithinAt hh (mapsTo_univ _ _)
 #align has_deriv_at.scomp_has_deriv_within_at HasDerivAt.scomp_hasDerivWithinAt
+-/
 
+#print derivWithin.scomp /-
 theorem derivWithin.scomp (hg : DifferentiableWithinAt 𝕜' g₁ t' (h x))
     (hh : DifferentiableWithinAt 𝕜 h s x) (hs : MapsTo h s t') (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (g₁ ∘ h) s x = derivWithin h s x • derivWithin g₁ t' (h x) :=
   (HasDerivWithinAt.scomp x hg.HasDerivWithinAt hh.HasDerivWithinAt hs).derivWithin hxs
 #align deriv_within.scomp derivWithin.scomp
+-/
 
+#print deriv.scomp /-
 theorem deriv.scomp (hg : DifferentiableAt 𝕜' g₁ (h x)) (hh : DifferentiableAt 𝕜 h x) :
     deriv (g₁ ∘ h) x = deriv h x • deriv g₁ (h x) :=
   (HasDerivAt.scomp x hg.HasDerivAt hh.HasDerivAt).deriv
 #align deriv.scomp deriv.scomp
+-/
 
 /-! ### Derivative of the composition of a scalar and vector functions -/
 
 
+#print HasDerivAtFilter.comp_hasFDerivAtFilter /-
 theorem HasDerivAtFilter.comp_hasFDerivAtFilter {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x) {L'' : Filter E}
     (hh₂ : HasDerivAtFilter h₂ h₂' (f x) L') (hf : HasFDerivAtFilter f f' x L'')
     (hL : Tendsto f L'' L') : HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') x L'' := by
   convert (hh₂.restrict_scalars 𝕜).comp x hf hL; ext x; simp [mul_comm]
 #align has_deriv_at_filter.comp_has_fderiv_at_filter HasDerivAtFilter.comp_hasFDerivAtFilter
+-/
 
+#print HasStrictDerivAt.comp_hasStrictFDerivAt /-
 theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
     (hh : HasStrictDerivAt h₂ h₂' (f x)) (hf : HasStrictFDerivAt f f' x) :
     HasStrictFDerivAt (h₂ ∘ f) (h₂' • f') x :=
@@ -141,90 +160,119 @@ theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[
   ext x
   simp [mul_comm]
 #align has_strict_deriv_at.comp_has_strict_fderiv_at HasStrictDerivAt.comp_hasStrictFDerivAt
+-/
 
+#print HasDerivAt.comp_hasFDerivAt /-
 theorem HasDerivAt.comp_hasFDerivAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
     (hh : HasDerivAt h₂ h₂' (f x)) (hf : HasFDerivAt f f' x) : HasFDerivAt (h₂ ∘ f) (h₂' • f') x :=
   hh.comp_hasFDerivAtFilter x hf hf.ContinuousAt
 #align has_deriv_at.comp_has_fderiv_at HasDerivAt.comp_hasFDerivAt
+-/
 
+#print HasDerivAt.comp_hasFDerivWithinAt /-
 theorem HasDerivAt.comp_hasFDerivWithinAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {s} (x)
     (hh : HasDerivAt h₂ h₂' (f x)) (hf : HasFDerivWithinAt f f' s x) :
     HasFDerivWithinAt (h₂ ∘ f) (h₂' • f') s x :=
   hh.comp_hasFDerivAtFilter x hf hf.ContinuousWithinAt
 #align has_deriv_at.comp_has_fderiv_within_at HasDerivAt.comp_hasFDerivWithinAt
+-/
 
+#print HasDerivWithinAt.comp_hasFDerivWithinAt /-
 theorem HasDerivWithinAt.comp_hasFDerivWithinAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {s t} (x)
     (hh : HasDerivWithinAt h₂ h₂' t (f x)) (hf : HasFDerivWithinAt f f' s x) (hst : MapsTo f s t) :
     HasFDerivWithinAt (h₂ ∘ f) (h₂' • f') s x :=
   hh.comp_hasFDerivAtFilter x hf <| hf.ContinuousWithinAt.tendsto_nhdsWithin hst
 #align has_deriv_within_at.comp_has_fderiv_within_at HasDerivWithinAt.comp_hasFDerivWithinAt
+-/
 
 /-! ### Derivative of the composition of two scalar functions -/
 
 
+#print HasDerivAtFilter.comp /-
 theorem HasDerivAtFilter.comp (hh₂ : HasDerivAtFilter h₂ h₂' (h x) L')
     (hh : HasDerivAtFilter h h' x L) (hL : Tendsto h L L') :
     HasDerivAtFilter (h₂ ∘ h) (h₂' * h') x L := by rw [mul_comm]; exact hh₂.scomp x hh hL
 #align has_deriv_at_filter.comp HasDerivAtFilter.comp
+-/
 
+#print HasDerivWithinAt.comp /-
 theorem HasDerivWithinAt.comp (hh₂ : HasDerivWithinAt h₂ h₂' s' (h x))
     (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s s') :
     HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x := by rw [mul_comm]; exact hh₂.scomp x hh hst
 #align has_deriv_within_at.comp HasDerivWithinAt.comp
+-/
 
+#print HasDerivAt.comp /-
 /-- The chain rule. -/
 theorem HasDerivAt.comp (hh₂ : HasDerivAt h₂ h₂' (h x)) (hh : HasDerivAt h h' x) :
     HasDerivAt (h₂ ∘ h) (h₂' * h') x :=
   hh₂.comp x hh hh.ContinuousAt
 #align has_deriv_at.comp HasDerivAt.comp
+-/
 
+#print HasStrictDerivAt.comp /-
 theorem HasStrictDerivAt.comp (hh₂ : HasStrictDerivAt h₂ h₂' (h x)) (hh : HasStrictDerivAt h h' x) :
     HasStrictDerivAt (h₂ ∘ h) (h₂' * h') x := by rw [mul_comm]; exact hh₂.scomp x hh
 #align has_strict_deriv_at.comp HasStrictDerivAt.comp
+-/
 
+#print HasDerivAt.comp_hasDerivWithinAt /-
 theorem HasDerivAt.comp_hasDerivWithinAt (hh₂ : HasDerivAt h₂ h₂' (h x))
     (hh : HasDerivWithinAt h h' s x) : HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x :=
   hh₂.HasDerivWithinAt.comp x hh (mapsTo_univ _ _)
 #align has_deriv_at.comp_has_deriv_within_at HasDerivAt.comp_hasDerivWithinAt
+-/
 
+#print derivWithin.comp /-
 theorem derivWithin.comp (hh₂ : DifferentiableWithinAt 𝕜' h₂ s' (h x))
     (hh : DifferentiableWithinAt 𝕜 h s x) (hs : MapsTo h s s') (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (h₂ ∘ h) s x = derivWithin h₂ s' (h x) * derivWithin h s x :=
   (hh₂.HasDerivWithinAt.comp x hh.HasDerivWithinAt hs).derivWithin hxs
 #align deriv_within.comp derivWithin.comp
+-/
 
+#print deriv.comp /-
 theorem deriv.comp (hh₂ : DifferentiableAt 𝕜' h₂ (h x)) (hh : DifferentiableAt 𝕜 h x) :
     deriv (h₂ ∘ h) x = deriv h₂ (h x) * deriv h x :=
   (hh₂.HasDerivAt.comp x hh.HasDerivAt).deriv
 #align deriv.comp deriv.comp
+-/
 
+#print HasDerivAtFilter.iterate /-
 protected theorem HasDerivAtFilter.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivAtFilter f f' x L)
     (hL : Tendsto f L L) (hx : f x = x) (n : ℕ) : HasDerivAtFilter (f^[n]) (f' ^ n) x L :=
   by
   have := hf.iterate hL hx n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_deriv_at_filter.iterate HasDerivAtFilter.iterate
+-/
 
+#print HasDerivAt.iterate /-
 protected theorem HasDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivAt f f' x) (hx : f x = x)
     (n : ℕ) : HasDerivAt (f^[n]) (f' ^ n) x :=
   by
   have := HasFDerivAt.iterate hf hx n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_deriv_at.iterate HasDerivAt.iterate
+-/
 
+#print HasDerivWithinAt.iterate /-
 protected theorem HasDerivWithinAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivWithinAt f f' s x)
     (hx : f x = x) (hs : MapsTo f s s) (n : ℕ) : HasDerivWithinAt (f^[n]) (f' ^ n) s x :=
   by
   have := HasFDerivWithinAt.iterate hf hx hs n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_deriv_within_at.iterate HasDerivWithinAt.iterate
+-/
 
+#print HasStrictDerivAt.iterate /-
 protected theorem HasStrictDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasStrictDerivAt f f' x)
     (hx : f x = x) (n : ℕ) : HasStrictDerivAt (f^[n]) (f' ^ n) x :=
   by
   have := hf.iterate hx n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_strict_deriv_at.iterate HasStrictDerivAt.iterate
+-/
 
 end Composition
 
@@ -239,6 +287,7 @@ variable {l : F → E} {l' : F →L[𝕜] E}
 
 variable (x)
 
+#print HasFDerivWithinAt.comp_hasDerivWithinAt /-
 /-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative within a set
 equal to the Fréchet derivative of `l` applied to the derivative of `f`. -/
 theorem HasFDerivWithinAt.comp_hasDerivWithinAt {t : Set F} (hl : HasFDerivWithinAt l l' t (f x))
@@ -247,35 +296,46 @@ theorem HasFDerivWithinAt.comp_hasDerivWithinAt {t : Set F} (hl : HasFDerivWithi
   simpa only [one_apply, one_smul, smul_right_apply, coe_comp', (· ∘ ·)] using
     (hl.comp x hf.has_fderiv_within_at hst).HasDerivWithinAt
 #align has_fderiv_within_at.comp_has_deriv_within_at HasFDerivWithinAt.comp_hasDerivWithinAt
+-/
 
+#print HasFDerivAt.comp_hasDerivWithinAt /-
 theorem HasFDerivAt.comp_hasDerivWithinAt (hl : HasFDerivAt l l' (f x))
     (hf : HasDerivWithinAt f f' s x) : HasDerivWithinAt (l ∘ f) (l' f') s x :=
   hl.HasFDerivWithinAt.comp_hasDerivWithinAt x hf (mapsTo_univ _ _)
 #align has_fderiv_at.comp_has_deriv_within_at HasFDerivAt.comp_hasDerivWithinAt
+-/
 
+#print HasFDerivAt.comp_hasDerivAt /-
 /-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative equal to the
 Fréchet derivative of `l` applied to the derivative of `f`. -/
 theorem HasFDerivAt.comp_hasDerivAt (hl : HasFDerivAt l l' (f x)) (hf : HasDerivAt f f' x) :
     HasDerivAt (l ∘ f) (l' f') x :=
   hasDerivWithinAt_univ.mp <| hl.comp_hasDerivWithinAt x hf.HasDerivWithinAt
 #align has_fderiv_at.comp_has_deriv_at HasFDerivAt.comp_hasDerivAt
+-/
 
+#print HasStrictFDerivAt.comp_hasStrictDerivAt /-
 theorem HasStrictFDerivAt.comp_hasStrictDerivAt (hl : HasStrictFDerivAt l l' (f x))
     (hf : HasStrictDerivAt f f' x) : HasStrictDerivAt (l ∘ f) (l' f') x := by
   simpa only [one_apply, one_smul, smul_right_apply, coe_comp', (· ∘ ·)] using
     (hl.comp x hf.has_strict_fderiv_at).HasStrictDerivAt
 #align has_strict_fderiv_at.comp_has_strict_deriv_at HasStrictFDerivAt.comp_hasStrictDerivAt
+-/
 
+#print fderivWithin.comp_derivWithin /-
 theorem fderivWithin.comp_derivWithin {t : Set F} (hl : DifferentiableWithinAt 𝕜 l t (f x))
     (hf : DifferentiableWithinAt 𝕜 f s x) (hs : MapsTo f s t) (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (l ∘ f) s x = (fderivWithin 𝕜 l t (f x) : F → E) (derivWithin f s x) :=
   (hl.HasFDerivWithinAt.comp_hasDerivWithinAt x hf.HasDerivWithinAt hs).derivWithin hxs
 #align fderiv_within.comp_deriv_within fderivWithin.comp_derivWithin
+-/
 
+#print fderiv.comp_deriv /-
 theorem fderiv.comp_deriv (hl : DifferentiableAt 𝕜 l (f x)) (hf : DifferentiableAt 𝕜 f x) :
     deriv (l ∘ f) x = (fderiv 𝕜 l (f x) : F → E) (deriv f x) :=
   (hl.HasFDerivAt.comp_hasDerivAt x hf.HasDerivAt).deriv
 #align fderiv.comp_deriv fderiv.comp_deriv
+-/
 
 end CompositionVector
 

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

@@ -129,7 +129,7 @@ theorem deriv.scomp (hg : DifferentiableAt 𝕜' g₁ (h x)) (hh : Differentiabl
 theorem HasDerivAtFilter.comp_hasFDerivAtFilter {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x) {L'' : Filter E}
     (hh₂ : HasDerivAtFilter h₂ h₂' (f x) L') (hf : HasFDerivAtFilter f f' x L'')
     (hL : Tendsto f L'' L') : HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') x L'' := by
-  convert(hh₂.restrict_scalars 𝕜).comp x hf hL; ext x; simp [mul_comm]
+  convert (hh₂.restrict_scalars 𝕜).comp x hf hL; ext x; simp [mul_comm]
 #align has_deriv_at_filter.comp_has_fderiv_at_filter HasDerivAtFilter.comp_hasFDerivAtFilter
 
 theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
@@ -137,7 +137,7 @@ theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[
     HasStrictFDerivAt (h₂ ∘ f) (h₂' • f') x :=
   by
   rw [HasStrictDerivAt] at hh 
-  convert(hh.restrict_scalars 𝕜).comp x hf
+  convert (hh.restrict_scalars 𝕜).comp x hf
   ext x
   simp [mul_comm]
 #align has_strict_deriv_at.comp_has_strict_fderiv_at HasStrictDerivAt.comp_hasStrictFDerivAt

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

@@ -136,7 +136,7 @@ theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[
     (hh : HasStrictDerivAt h₂ h₂' (f x)) (hf : HasStrictFDerivAt f f' x) :
     HasStrictFDerivAt (h₂ ∘ f) (h₂' • f') x :=
   by
-  rw [HasStrictDerivAt] at hh
+  rw [HasStrictDerivAt] at hh 
   convert(hh.restrict_scalars 𝕜).comp x hf
   ext x
   simp [mul_comm]
@@ -202,28 +202,28 @@ protected theorem HasDerivAtFilter.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf :
     (hL : Tendsto f L L) (hx : f x = x) (n : ℕ) : HasDerivAtFilter (f^[n]) (f' ^ n) x L :=
   by
   have := hf.iterate hL hx n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_deriv_at_filter.iterate HasDerivAtFilter.iterate
 
 protected theorem HasDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivAt f f' x) (hx : f x = x)
     (n : ℕ) : HasDerivAt (f^[n]) (f' ^ n) x :=
   by
   have := HasFDerivAt.iterate hf hx n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_deriv_at.iterate HasDerivAt.iterate
 
 protected theorem HasDerivWithinAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivWithinAt f f' s x)
     (hx : f x = x) (hs : MapsTo f s s) (n : ℕ) : HasDerivWithinAt (f^[n]) (f' ^ n) s x :=
   by
   have := HasFDerivWithinAt.iterate hf hx hs n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_deriv_within_at.iterate HasDerivWithinAt.iterate
 
 protected theorem HasStrictDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasStrictDerivAt f f' x)
     (hx : f x = x) (n : ℕ) : HasStrictDerivAt (f^[n]) (f' ^ n) x :=
   by
   have := hf.iterate hx n
-  rwa [ContinuousLinearMap.smulRight_one_pow] at this
+  rwa [ContinuousLinearMap.smulRight_one_pow] at this 
 #align has_strict_deriv_at.iterate HasStrictDerivAt.iterate
 
 end Composition

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: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao
 
 ! This file was ported from Lean 3 source module analysis.calculus.deriv.comp
-! 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.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.Calculus.Fderiv.RestrictScalars
 /-!
 # One-dimensional derivatives of compositions of functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove the chain rule for the following cases:
 
 * `has_deriv_at.comp` etc: `f : 𝕜' → 𝕜'` composed with `g : 𝕜 → 𝕜'`;

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

@@ -35,7 +35,7 @@ derivative, chain rule
 
 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

@@ -125,11 +125,8 @@ theorem deriv.scomp (hg : DifferentiableAt 𝕜' g₁ (h x)) (hh : Differentiabl
 
 theorem HasDerivAtFilter.comp_hasFDerivAtFilter {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x) {L'' : Filter E}
     (hh₂ : HasDerivAtFilter h₂ h₂' (f x) L') (hf : HasFDerivAtFilter f f' x L'')
-    (hL : Tendsto f L'' L') : HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') x L'' :=
-  by
-  convert(hh₂.restrict_scalars 𝕜).comp x hf hL
-  ext x
-  simp [mul_comm]
+    (hL : Tendsto f L'' L') : HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') x L'' := by
+  convert(hh₂.restrict_scalars 𝕜).comp x hf hL; ext x; simp [mul_comm]
 #align has_deriv_at_filter.comp_has_fderiv_at_filter HasDerivAtFilter.comp_hasFDerivAtFilter
 
 theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
@@ -164,18 +161,12 @@ theorem HasDerivWithinAt.comp_hasFDerivWithinAt {f : E → 𝕜'} {f' : E →L[
 
 theorem HasDerivAtFilter.comp (hh₂ : HasDerivAtFilter h₂ h₂' (h x) L')
     (hh : HasDerivAtFilter h h' x L) (hL : Tendsto h L L') :
-    HasDerivAtFilter (h₂ ∘ h) (h₂' * h') x L :=
-  by
-  rw [mul_comm]
-  exact hh₂.scomp x hh hL
+    HasDerivAtFilter (h₂ ∘ h) (h₂' * h') x L := by rw [mul_comm]; exact hh₂.scomp x hh hL
 #align has_deriv_at_filter.comp HasDerivAtFilter.comp
 
 theorem HasDerivWithinAt.comp (hh₂ : HasDerivWithinAt h₂ h₂' s' (h x))
     (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s s') :
-    HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x :=
-  by
-  rw [mul_comm]
-  exact hh₂.scomp x hh hst
+    HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x := by rw [mul_comm]; exact hh₂.scomp x hh hst
 #align has_deriv_within_at.comp HasDerivWithinAt.comp
 
 /-- The chain rule. -/
@@ -185,10 +176,7 @@ theorem HasDerivAt.comp (hh₂ : HasDerivAt h₂ h₂' (h x)) (hh : HasDerivAt h
 #align has_deriv_at.comp HasDerivAt.comp
 
 theorem HasStrictDerivAt.comp (hh₂ : HasStrictDerivAt h₂ h₂' (h x)) (hh : HasStrictDerivAt h h' x) :
-    HasStrictDerivAt (h₂ ∘ h) (h₂' * h') x :=
-  by
-  rw [mul_comm]
-  exact hh₂.scomp x hh
+    HasStrictDerivAt (h₂ ∘ h) (h₂' * h') x := by rw [mul_comm]; exact hh₂.scomp x hh
 #align has_strict_deriv_at.comp HasStrictDerivAt.comp
 
 theorem HasDerivAt.comp_hasDerivWithinAt (hh₂ : HasDerivAt h₂ h₂' (h x))

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

The versions we have assume that f is differentiable at h x and h is differentiable at x, to deduce that f o h is differentiable at x. In many applications, we have that f is differentiable at some point which happens to be equal to h x, but not definitionally, so one needs to jump through some hoops to apply the composition lemma. We add of_eq versions assuming instead that f is differentiable at y and that y = h x, which is much more flexible in practice.

@@ -21,6 +21,10 @@ In this file we prove the chain rule for the following cases:
 Here `𝕜` is the base normed field, `E` and `F` are normed spaces over `𝕜` and `𝕜'` is an algebra
 over `𝕜` (e.g., `𝕜'=𝕜` or `𝕜=ℝ`, `𝕜'=ℂ`).
 
+We also give versions with the `of_eq` suffix, which require an equality proof instead
+of definitional equality of the different points used in the composition. These versions are
+often more flexible to use.
+
 For a more detailed overview of one-dimensional derivatives in mathlib, see the module docstring of
 `analysis/calculus/deriv/basic`.
 
@@ -65,7 +69,7 @@ usual multiplication in `comp` lemmas.
 get confused since there are too many possibilities for composition -/
 variable {𝕜' : Type*} [NontriviallyNormedField 𝕜'] [NormedAlgebra 𝕜 𝕜'] [NormedSpace 𝕜' F]
   [IsScalarTower 𝕜 𝕜' F] {s' t' : Set 𝕜'} {h : 𝕜 → 𝕜'} {h₁ : 𝕜 → 𝕜} {h₂ : 𝕜' → 𝕜'} {h' h₂' : 𝕜'}
-  {h₁' : 𝕜} {g₁ : 𝕜' → F} {g₁' : F} {L' : Filter 𝕜'} (x)
+  {h₁' : 𝕜} {g₁ : 𝕜' → F} {g₁' : F} {L' : Filter 𝕜'} {y : 𝕜'} (x)
 
 theorem HasDerivAtFilter.scomp (hg : HasDerivAtFilter g₁ g₁' (h x) L')
     (hh : HasDerivAtFilter h h' x L) (hL : Tendsto h L L') :
@@ -73,46 +77,87 @@ theorem HasDerivAtFilter.scomp (hg : HasDerivAtFilter g₁ g₁' (h x) L')
   simpa using ((hg.restrictScalars 𝕜).comp x hh hL).hasDerivAtFilter
 #align has_deriv_at_filter.scomp HasDerivAtFilter.scomp
 
+theorem HasDerivAtFilter.scomp_of_eq (hg : HasDerivAtFilter g₁ g₁' y L')
+    (hh : HasDerivAtFilter h h' x L) (hy : y = h x) (hL : Tendsto h L L') :
+    HasDerivAtFilter (g₁ ∘ h) (h' • g₁') x L := by
+  rw [hy] at hg; exact hg.scomp x hh hL
+
 theorem HasDerivWithinAt.scomp_hasDerivAt (hg : HasDerivWithinAt g₁ g₁' s' (h x))
     (hh : HasDerivAt h h' x) (hs : ∀ x, h x ∈ s') : HasDerivAt (g₁ ∘ h) (h' • g₁') x :=
   hg.scomp x hh <| tendsto_inf.2 ⟨hh.continuousAt, tendsto_principal.2 <| eventually_of_forall hs⟩
 #align has_deriv_within_at.scomp_has_deriv_at HasDerivWithinAt.scomp_hasDerivAt
 
+theorem HasDerivWithinAt.scomp_hasDerivAt_of_eq (hg : HasDerivWithinAt g₁ g₁' s' y)
+    (hh : HasDerivAt h h' x) (hs : ∀ x, h x ∈ s') (hy : y = h x) :
+    HasDerivAt (g₁ ∘ h) (h' • g₁') x := by
+  rw [hy] at hg; exact hg.scomp_hasDerivAt x hh hs
+
 nonrec theorem HasDerivWithinAt.scomp (hg : HasDerivWithinAt g₁ g₁' t' (h x))
     (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s t') :
     HasDerivWithinAt (g₁ ∘ h) (h' • g₁') s x :=
   hg.scomp x hh <| hh.continuousWithinAt.tendsto_nhdsWithin hst
 #align has_deriv_within_at.scomp HasDerivWithinAt.scomp
 
+theorem HasDerivWithinAt.scomp_of_eq (hg : HasDerivWithinAt g₁ g₁' t' y)
+    (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s t') (hy : y = h x) :
+    HasDerivWithinAt (g₁ ∘ h) (h' • g₁') s x := by
+  rw [hy] at hg; exact hg.scomp x hh hst
+
 /-- The chain rule. -/
 nonrec theorem HasDerivAt.scomp (hg : HasDerivAt g₁ g₁' (h x)) (hh : HasDerivAt h h' x) :
     HasDerivAt (g₁ ∘ h) (h' • g₁') x :=
   hg.scomp x hh hh.continuousAt
 #align has_deriv_at.scomp HasDerivAt.scomp
 
+/-- The chain rule. -/
+theorem HasDerivAt.scomp_of_eq
+    (hg : HasDerivAt g₁ g₁' y) (hh : HasDerivAt h h' x) (hy : y = h x) :
+    HasDerivAt (g₁ ∘ h) (h' • g₁') x := by
+  rw [hy] at hg; exact hg.scomp x hh
+
 theorem HasStrictDerivAt.scomp (hg : HasStrictDerivAt g₁ g₁' (h x)) (hh : HasStrictDerivAt h h' x) :
     HasStrictDerivAt (g₁ ∘ h) (h' • g₁') x := by
   simpa using ((hg.restrictScalars 𝕜).comp x hh).hasStrictDerivAt
 #align has_strict_deriv_at.scomp HasStrictDerivAt.scomp
 
+theorem HasStrictDerivAt.scomp_of_eq
+    (hg : HasStrictDerivAt g₁ g₁' y) (hh : HasStrictDerivAt h h' x) (hy : y = h x) :
+    HasStrictDerivAt (g₁ ∘ h) (h' • g₁') x := by
+  rw [hy] at hg; exact hg.scomp x hh
+
 theorem HasDerivAt.scomp_hasDerivWithinAt (hg : HasDerivAt g₁ g₁' (h x))
     (hh : HasDerivWithinAt h h' s x) : HasDerivWithinAt (g₁ ∘ h) (h' • g₁') s x :=
   HasDerivWithinAt.scomp x hg.hasDerivWithinAt hh (mapsTo_univ _ _)
 #align has_deriv_at.scomp_has_deriv_within_at HasDerivAt.scomp_hasDerivWithinAt
 
+theorem HasDerivAt.scomp_hasDerivWithinAt_of_eq (hg : HasDerivAt g₁ g₁' y)
+    (hh : HasDerivWithinAt h h' s x) (hy : y = h x) :
+    HasDerivWithinAt (g₁ ∘ h) (h' • g₁') s x := by
+  rw [hy] at hg; exact hg.scomp_hasDerivWithinAt x hh
+
 theorem derivWithin.scomp (hg : DifferentiableWithinAt 𝕜' g₁ t' (h x))
     (hh : DifferentiableWithinAt 𝕜 h s x) (hs : MapsTo h s t') (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (g₁ ∘ h) s x = derivWithin h s x • derivWithin g₁ t' (h x) :=
   (HasDerivWithinAt.scomp x hg.hasDerivWithinAt hh.hasDerivWithinAt hs).derivWithin hxs
 #align deriv_within.scomp derivWithin.scomp
 
+theorem derivWithin.scomp_of_eq (hg : DifferentiableWithinAt 𝕜' g₁ t' y)
+    (hh : DifferentiableWithinAt 𝕜 h s x) (hs : MapsTo h s t') (hxs : UniqueDiffWithinAt 𝕜 s x)
+    (hy : y = h x) :
+    derivWithin (g₁ ∘ h) s x = derivWithin h s x • derivWithin g₁ t' (h x) := by
+  rw [hy] at hg; exact derivWithin.scomp x hg hh hs hxs
+
 theorem deriv.scomp (hg : DifferentiableAt 𝕜' g₁ (h x)) (hh : DifferentiableAt 𝕜 h x) :
     deriv (g₁ ∘ h) x = deriv h x • deriv g₁ (h x) :=
   (HasDerivAt.scomp x hg.hasDerivAt hh.hasDerivAt).deriv
 #align deriv.scomp deriv.scomp
 
-/-! ### Derivative of the composition of a scalar and vector functions -/
+theorem deriv.scomp_of_eq
+    (hg : DifferentiableAt 𝕜' g₁ y) (hh : DifferentiableAt 𝕜 h x) (hy : y = h x) :
+    deriv (g₁ ∘ h) x = deriv h x • deriv g₁ (h x) := by
+  rw [hy] at hg; exact deriv.scomp x hg hh
 
+/-! ### Derivative of the composition of a scalar and vector functions -/
 
 theorem HasDerivAtFilter.comp_hasFDerivAtFilter {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x) {L'' : Filter E}
     (hh₂ : HasDerivAtFilter h₂ h₂' (f x) L') (hf : HasFDerivAtFilter f f' x L'')
@@ -122,6 +167,12 @@ theorem HasDerivAtFilter.comp_hasFDerivAtFilter {f : E → 𝕜'} {f' : E →L[
   simp [mul_comm]
 #align has_deriv_at_filter.comp_has_fderiv_at_filter HasDerivAtFilter.comp_hasFDerivAtFilter
 
+theorem HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq
+    {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x) {L'' : Filter E}
+    (hh₂ : HasDerivAtFilter h₂ h₂' y L') (hf : HasFDerivAtFilter f f' x L'')
+    (hL : Tendsto f L'' L') (hy : y = f x) : HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') x L'' := by
+  rw [hy] at hh₂; exact hh₂.comp_hasFDerivAtFilter x hf hL
+
 theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
     (hh : HasStrictDerivAt h₂ h₂' (f x)) (hf : HasStrictFDerivAt f f' x) :
     HasStrictFDerivAt (h₂ ∘ f) (h₂' • f') x := by
@@ -131,23 +182,44 @@ theorem HasStrictDerivAt.comp_hasStrictFDerivAt {f : E → 𝕜'} {f' : E →L[
   simp [mul_comm]
 #align has_strict_deriv_at.comp_has_strict_fderiv_at HasStrictDerivAt.comp_hasStrictFDerivAt
 
+theorem HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
+    (hh : HasStrictDerivAt h₂ h₂' y) (hf : HasStrictFDerivAt f f' x) (hy : y = f x) :
+    HasStrictFDerivAt (h₂ ∘ f) (h₂' • f') x := by
+  rw [hy] at hh; exact hh.comp_hasStrictFDerivAt x hf
+
 theorem HasDerivAt.comp_hasFDerivAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
     (hh : HasDerivAt h₂ h₂' (f x)) (hf : HasFDerivAt f f' x) : HasFDerivAt (h₂ ∘ f) (h₂' • f') x :=
   hh.comp_hasFDerivAtFilter x hf hf.continuousAt
 #align has_deriv_at.comp_has_fderiv_at HasDerivAt.comp_hasFDerivAt
 
+theorem HasDerivAt.comp_hasFDerivAt_of_eq {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x)
+    (hh : HasDerivAt h₂ h₂' y) (hf : HasFDerivAt f f' x) (hy : y = f x) :
+    HasFDerivAt (h₂ ∘ f) (h₂' • f') x := by
+  rw [hy] at hh; exact hh.comp_hasFDerivAt x hf
+
 theorem HasDerivAt.comp_hasFDerivWithinAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {s} (x)
     (hh : HasDerivAt h₂ h₂' (f x)) (hf : HasFDerivWithinAt f f' s x) :
     HasFDerivWithinAt (h₂ ∘ f) (h₂' • f') s x :=
   hh.comp_hasFDerivAtFilter x hf hf.continuousWithinAt
 #align has_deriv_at.comp_has_fderiv_within_at HasDerivAt.comp_hasFDerivWithinAt
 
+theorem HasDerivAt.comp_hasFDerivWithinAt_of_eq {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {s} (x)
+    (hh : HasDerivAt h₂ h₂' y) (hf : HasFDerivWithinAt f f' s x) (hy : y = f x) :
+    HasFDerivWithinAt (h₂ ∘ f) (h₂' • f') s x := by
+  rw [hy] at hh; exact hh.comp_hasFDerivWithinAt x hf
+
 theorem HasDerivWithinAt.comp_hasFDerivWithinAt {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {s t} (x)
     (hh : HasDerivWithinAt h₂ h₂' t (f x)) (hf : HasFDerivWithinAt f f' s x) (hst : MapsTo f s t) :
     HasFDerivWithinAt (h₂ ∘ f) (h₂' • f') s x :=
   hh.comp_hasFDerivAtFilter x hf <| hf.continuousWithinAt.tendsto_nhdsWithin hst
 #align has_deriv_within_at.comp_has_fderiv_within_at HasDerivWithinAt.comp_hasFDerivWithinAt
 
+theorem HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {s t} (x)
+    (hh : HasDerivWithinAt h₂ h₂' t y) (hf : HasFDerivWithinAt f f' s x) (hst : MapsTo f s t)
+    (hy : y = f x) :
+    HasFDerivWithinAt (h₂ ∘ f) (h₂' • f') s x := by
+  rw [hy] at hh; exact hh.comp_hasFDerivWithinAt x hf hst
+
 /-! ### Derivative of the composition of two scalar functions -/
 
 theorem HasDerivAtFilter.comp (hh₂ : HasDerivAtFilter h₂ h₂' (h x) L')
@@ -157,6 +229,11 @@ theorem HasDerivAtFilter.comp (hh₂ : HasDerivAtFilter h₂ h₂' (h x) L')
   exact hh₂.scomp x hh hL
 #align has_deriv_at_filter.comp HasDerivAtFilter.comp
 
+theorem HasDerivAtFilter.comp_of_eq (hh₂ : HasDerivAtFilter h₂ h₂' y L')
+    (hh : HasDerivAtFilter h h' x L) (hL : Tendsto h L L') (hy : y = h x) :
+    HasDerivAtFilter (h₂ ∘ h) (h₂' * h') x L := by
+  rw [hy] at hh₂; exact hh₂.comp x hh hL
+
 theorem HasDerivWithinAt.comp (hh₂ : HasDerivWithinAt h₂ h₂' s' (h x))
     (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s s') :
     HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x := by
@@ -164,34 +241,72 @@ theorem HasDerivWithinAt.comp (hh₂ : HasDerivWithinAt h₂ h₂' s' (h x))
   exact hh₂.scomp x hh hst
 #align has_deriv_within_at.comp HasDerivWithinAt.comp
 
-/-- The chain rule. -/
+theorem HasDerivWithinAt.comp_of_eq (hh₂ : HasDerivWithinAt h₂ h₂' s' y)
+    (hh : HasDerivWithinAt h h' s x) (hst : MapsTo h s s') (hy : y = h x) :
+    HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x := by
+  rw [hy] at hh₂; exact hh₂.comp x hh hst
+
+/-- The chain rule.
+
+Note that the function `h₂` is a function on an algebra. If you are looking for the chain rule
+with `h₂` taking values in a vector space, use `HasDerivAt.scomp`. -/
 nonrec theorem HasDerivAt.comp (hh₂ : HasDerivAt h₂ h₂' (h x)) (hh : HasDerivAt h h' x) :
     HasDerivAt (h₂ ∘ h) (h₂' * h') x :=
   hh₂.comp x hh hh.continuousAt
 #align has_deriv_at.comp HasDerivAt.comp
 
+/-- The chain rule.
+
+Note that the function `h₂` is a function on an algebra. If you are looking for the chain rule
+with `h₂` taking values in a vector space, use `HasDerivAt.scomp_of_eq`. -/
+theorem HasDerivAt.comp_of_eq
+    (hh₂ : HasDerivAt h₂ h₂' y) (hh : HasDerivAt h h' x) (hy : y = h x) :
+    HasDerivAt (h₂ ∘ h) (h₂' * h') x := by
+  rw [hy] at hh₂; exact hh₂.comp x hh
+
 theorem HasStrictDerivAt.comp (hh₂ : HasStrictDerivAt h₂ h₂' (h x)) (hh : HasStrictDerivAt h h' x) :
     HasStrictDerivAt (h₂ ∘ h) (h₂' * h') x := by
   rw [mul_comm]
   exact hh₂.scomp x hh
 #align has_strict_deriv_at.comp HasStrictDerivAt.comp
 
+theorem HasStrictDerivAt.comp_of_eq
+    (hh₂ : HasStrictDerivAt h₂ h₂' y) (hh : HasStrictDerivAt h h' x) (hy : y = h x) :
+    HasStrictDerivAt (h₂ ∘ h) (h₂' * h') x := by
+  rw [hy] at hh₂; exact hh₂.comp x hh
+
 theorem HasDerivAt.comp_hasDerivWithinAt (hh₂ : HasDerivAt h₂ h₂' (h x))
     (hh : HasDerivWithinAt h h' s x) : HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x :=
   hh₂.hasDerivWithinAt.comp x hh (mapsTo_univ _ _)
 #align has_deriv_at.comp_has_deriv_within_at HasDerivAt.comp_hasDerivWithinAt
 
+theorem HasDerivAt.comp_hasDerivWithinAt_of_eq (hh₂ : HasDerivAt h₂ h₂' y)
+    (hh : HasDerivWithinAt h h' s x) (hy : y = h x) :
+    HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x := by
+  rw [hy] at hh₂; exact hh₂.comp_hasDerivWithinAt x hh
+
 theorem derivWithin.comp (hh₂ : DifferentiableWithinAt 𝕜' h₂ s' (h x))
     (hh : DifferentiableWithinAt 𝕜 h s x) (hs : MapsTo h s s') (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (h₂ ∘ h) s x = derivWithin h₂ s' (h x) * derivWithin h s x :=
   (hh₂.hasDerivWithinAt.comp x hh.hasDerivWithinAt hs).derivWithin hxs
 #align deriv_within.comp derivWithin.comp
 
+theorem derivWithin.comp_of_eq (hh₂ : DifferentiableWithinAt 𝕜' h₂ s' y)
+    (hh : DifferentiableWithinAt 𝕜 h s x) (hs : MapsTo h s s') (hxs : UniqueDiffWithinAt 𝕜 s x)
+    (hy : y = h x) :
+    derivWithin (h₂ ∘ h) s x = derivWithin h₂ s' (h x) * derivWithin h s x := by
+  rw [hy] at hh₂; exact derivWithin.comp x hh₂ hh hs hxs
+
 theorem deriv.comp (hh₂ : DifferentiableAt 𝕜' h₂ (h x)) (hh : DifferentiableAt 𝕜 h x) :
     deriv (h₂ ∘ h) x = deriv h₂ (h x) * deriv h x :=
   (hh₂.hasDerivAt.comp x hh.hasDerivAt).deriv
 #align deriv.comp deriv.comp
 
+theorem deriv.comp_of_eq (hh₂ : DifferentiableAt 𝕜' h₂ y) (hh : DifferentiableAt 𝕜 h x)
+    (hy : y = h x) :
+    deriv (h₂ ∘ h) x = deriv h₂ (h x) * deriv h x := by
+  rw [hy] at hh₂; exact deriv.comp x hh₂ hh
+
 protected nonrec theorem HasDerivAtFilter.iterate {f : 𝕜 → 𝕜} {f' : 𝕜}
     (hf : HasDerivAtFilter f f' x L) (hL : Tendsto f L L) (hx : f x = x) (n : ℕ) :
     HasDerivAtFilter f^[n] (f' ^ n) x L := by
@@ -225,7 +340,7 @@ section CompositionVector
 
 open ContinuousLinearMap
 
-variable {l : F → E} {l' : F →L[𝕜] E}
+variable {l : F → E} {l' : F →L[𝕜] E} {y : F}
 variable (x)
 
 /-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative within a set
@@ -237,11 +352,24 @@ theorem HasFDerivWithinAt.comp_hasDerivWithinAt {t : Set F} (hl : HasFDerivWithi
     (hl.comp x hf.hasFDerivWithinAt hst).hasDerivWithinAt
 #align has_fderiv_within_at.comp_has_deriv_within_at HasFDerivWithinAt.comp_hasDerivWithinAt
 
+/-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative within a set
+equal to the Fréchet derivative of `l` applied to the derivative of `f`. -/
+theorem HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq {t : Set F}
+    (hl : HasFDerivWithinAt l l' t y)
+    (hf : HasDerivWithinAt f f' s x) (hst : MapsTo f s t) (hy : y = f x) :
+    HasDerivWithinAt (l ∘ f) (l' f') s x := by
+  rw [hy] at hl; exact hl.comp_hasDerivWithinAt x hf hst
+
 theorem HasFDerivAt.comp_hasDerivWithinAt (hl : HasFDerivAt l l' (f x))
     (hf : HasDerivWithinAt f f' s x) : HasDerivWithinAt (l ∘ f) (l' f') s x :=
   hl.hasFDerivWithinAt.comp_hasDerivWithinAt x hf (mapsTo_univ _ _)
 #align has_fderiv_at.comp_has_deriv_within_at HasFDerivAt.comp_hasDerivWithinAt
 
+theorem HasFDerivAt.comp_hasDerivWithinAt_of_eq (hl : HasFDerivAt l l' y)
+    (hf : HasDerivWithinAt f f' s x) (hy : y = f x) :
+    HasDerivWithinAt (l ∘ f) (l' f') s x := by
+  rw [hy] at hl; exact hl.comp_hasDerivWithinAt x hf
+
 /-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative equal to the
 Fréchet derivative of `l` applied to the derivative of `f`. -/
 theorem HasFDerivAt.comp_hasDerivAt (hl : HasFDerivAt l l' (f x)) (hf : HasDerivAt f f' x) :
@@ -249,21 +377,44 @@ theorem HasFDerivAt.comp_hasDerivAt (hl : HasFDerivAt l l' (f x)) (hf : HasDeriv
   hasDerivWithinAt_univ.mp <| hl.comp_hasDerivWithinAt x hf.hasDerivWithinAt
 #align has_fderiv_at.comp_has_deriv_at HasFDerivAt.comp_hasDerivAt
 
+/-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative equal to the
+Fréchet derivative of `l` applied to the derivative of `f`. -/
+theorem HasFDerivAt.comp_hasDerivAt_of_eq
+    (hl : HasFDerivAt l l' y) (hf : HasDerivAt f f' x) (hy : y = f x) :
+    HasDerivAt (l ∘ f) (l' f') x := by
+  rw [hy] at hl; exact hl.comp_hasDerivAt x hf
+
 theorem HasStrictFDerivAt.comp_hasStrictDerivAt (hl : HasStrictFDerivAt l l' (f x))
     (hf : HasStrictDerivAt f f' x) : HasStrictDerivAt (l ∘ f) (l' f') x := by
   simpa only [one_apply, one_smul, smulRight_apply, coe_comp', (· ∘ ·)] using
     (hl.comp x hf.hasStrictFDerivAt).hasStrictDerivAt
 #align has_strict_fderiv_at.comp_has_strict_deriv_at HasStrictFDerivAt.comp_hasStrictDerivAt
 
+theorem HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq (hl : HasStrictFDerivAt l l' y)
+    (hf : HasStrictDerivAt f f' x) (hy : y = f x) :
+    HasStrictDerivAt (l ∘ f) (l' f') x := by
+  rw [hy] at hl; exact hl.comp_hasStrictDerivAt x hf
+
 theorem fderivWithin.comp_derivWithin {t : Set F} (hl : DifferentiableWithinAt 𝕜 l t (f x))
     (hf : DifferentiableWithinAt 𝕜 f s x) (hs : MapsTo f s t) (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (l ∘ f) s x = (fderivWithin 𝕜 l t (f x) : F → E) (derivWithin f s x) :=
   (hl.hasFDerivWithinAt.comp_hasDerivWithinAt x hf.hasDerivWithinAt hs).derivWithin hxs
 #align fderiv_within.comp_deriv_within fderivWithin.comp_derivWithin
 
+theorem fderivWithin.comp_derivWithin_of_eq {t : Set F} (hl : DifferentiableWithinAt 𝕜 l t y)
+    (hf : DifferentiableWithinAt 𝕜 f s x) (hs : MapsTo f s t) (hxs : UniqueDiffWithinAt 𝕜 s x)
+    (hy : y = f x) :
+    derivWithin (l ∘ f) s x = (fderivWithin 𝕜 l t (f x) : F → E) (derivWithin f s x) := by
+  rw [hy] at hl; exact fderivWithin.comp_derivWithin x hl hf hs hxs
+
 theorem fderiv.comp_deriv (hl : DifferentiableAt 𝕜 l (f x)) (hf : DifferentiableAt 𝕜 f x) :
     deriv (l ∘ f) x = (fderiv 𝕜 l (f x) : F → E) (deriv f x) :=
   (hl.hasFDerivAt.comp_hasDerivAt x hf.hasDerivAt).deriv
 #align fderiv.comp_deriv fderiv.comp_deriv
 
+theorem fderiv.comp_deriv_of_eq (hl : DifferentiableAt 𝕜 l y) (hf : DifferentiableAt 𝕜 f x)
+    (hy : y = f x) :
+    deriv (l ∘ f) x = (fderiv 𝕜 l (f x) : F → E) (deriv f x) := by
+  rw [hy] at hl; exact fderiv.comp_deriv x hl hf
+
 end CompositionVector

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)

@@ -40,19 +40,12 @@ open Filter Asymptotics Set
 open ContinuousLinearMap (smulRight smulRight_one_eq_iff)
 
 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}
 
 section Composition
@@ -233,7 +226,6 @@ section CompositionVector
 open ContinuousLinearMap
 
 variable {l : F → E} {l' : F →L[𝕜] E}
-
 variable (x)
 
 /-- The composition `l ∘ f` where `l : F → E` and `f : 𝕜 → F`, has a derivative within a set

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.

@@ -32,7 +32,8 @@ derivative, chain rule
 
 universe u v w
 
-open Classical Topology BigOperators Filter ENNReal
+open scoped Classical
+open Topology BigOperators Filter ENNReal
 
 open Filter Asymptotics Set
 

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -69,7 +69,7 @@ usual multiplication in `comp` lemmas.
 
 /- For composition lemmas, we put x explicit to help the elaborator, as otherwise Lean tends to
 get confused since there are too many possibilities for composition -/
-variable {𝕜' : Type _} [NontriviallyNormedField 𝕜'] [NormedAlgebra 𝕜 𝕜'] [NormedSpace 𝕜' F]
+variable {𝕜' : Type*} [NontriviallyNormedField 𝕜'] [NormedAlgebra 𝕜 𝕜'] [NormedSpace 𝕜' F]
   [IsScalarTower 𝕜 𝕜' F] {s' t' : Set 𝕜'} {h : 𝕜 → 𝕜'} {h₁ : 𝕜 → 𝕜} {h₂ : 𝕜' → 𝕜'} {h' h₂' : 𝕜'}
   {h₁' : 𝕜} {g₁ : 𝕜' → F} {g₁' : F} {L' : Filter 𝕜'} (x)
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Gabriel Ebner. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao
-
-! This file was ported from Lean 3 source module analysis.calculus.deriv.comp
-! 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.Basic
 import Mathlib.Analysis.Calculus.FDeriv.Comp
 import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars
 
+#align_import analysis.calculus.deriv.comp from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-!
 # One-dimensional derivatives of compositions of functions
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -219,7 +219,7 @@ protected theorem HasDerivWithinAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf :
   rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_deriv_within_at.iterate HasDerivWithinAt.iterate
 
-protected nonrec  theorem HasStrictDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜}
+protected nonrec theorem HasStrictDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜}
     (hf : HasStrictDerivAt f f' x) (hx : f x = x) (n : ℕ) :
     HasStrictDerivAt f^[n] (f' ^ n) x := by
   have := hf.iterate hx n

@@ -203,25 +203,25 @@ theorem deriv.comp (hh₂ : DifferentiableAt 𝕜' h₂ (h x)) (hh : Differentia
 
 protected nonrec theorem HasDerivAtFilter.iterate {f : 𝕜 → 𝕜} {f' : 𝕜}
     (hf : HasDerivAtFilter f f' x L) (hL : Tendsto f L L) (hx : f x = x) (n : ℕ) :
-    HasDerivAtFilter (f^[n]) (f' ^ n) x L := by
+    HasDerivAtFilter f^[n] (f' ^ n) x L := by
   have := hf.iterate hL hx n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_deriv_at_filter.iterate HasDerivAtFilter.iterate
 
 protected nonrec theorem HasDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivAt f f' x)
-    (hx : f x = x) (n : ℕ) : HasDerivAt (f^[n]) (f' ^ n) x :=
+    (hx : f x = x) (n : ℕ) : HasDerivAt f^[n] (f' ^ n) x :=
   hf.iterate _ (have := hf.tendsto_nhds le_rfl; by rwa [hx] at this) hx n
 #align has_deriv_at.iterate HasDerivAt.iterate
 
 protected theorem HasDerivWithinAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜} (hf : HasDerivWithinAt f f' s x)
-    (hx : f x = x) (hs : MapsTo f s s) (n : ℕ) : HasDerivWithinAt (f^[n]) (f' ^ n) s x := by
+    (hx : f x = x) (hs : MapsTo f s s) (n : ℕ) : HasDerivWithinAt f^[n] (f' ^ n) s x := by
   have := HasFDerivWithinAt.iterate hf hx hs n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_deriv_within_at.iterate HasDerivWithinAt.iterate
 
 protected nonrec  theorem HasStrictDerivAt.iterate {f : 𝕜 → 𝕜} {f' : 𝕜}
     (hf : HasStrictDerivAt f f' x) (hx : f x = x) (n : ℕ) :
-    HasStrictDerivAt (f^[n]) (f' ^ n) x := by
+    HasStrictDerivAt f^[n] (f' ^ n) x := by
   have := hf.iterate hx n
   rwa [ContinuousLinearMap.smulRight_one_pow] at this
 #align has_strict_deriv_at.iterate HasStrictDerivAt.iterate
@@ -277,4 +277,3 @@ theorem fderiv.comp_deriv (hl : DifferentiableAt 𝕜 l (f x)) (hf : Differentia
 #align fderiv.comp_deriv fderiv.comp_deriv
 
 end CompositionVector
-