analysis.calculus.iterated_deriv ⟷ Mathlib.Analysis.Calculus.IteratedDeriv.Defs

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: Sébastien Gouëzel
 -/
 import Analysis.Calculus.Deriv.Comp
-import Analysis.Calculus.ContDiffDef
+import Analysis.Calculus.ContDiff.Defs
 
 #align_import analysis.calculus.iterated_deriv from "leanprover-community/mathlib"@"2ebc1d6c2fed9f54c95bbc3998eaa5570527129a"
 

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

@@ -230,7 +230,7 @@ theorem iteratedDerivWithin_succ {x : 𝕜} (hxs : UniqueDiffWithinAt 𝕜 s x)
   rw [iteratedDerivWithin_eq_iteratedFDerivWithin, iteratedFDerivWithin_succ_apply_left,
     iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_fderivWithin _ hxs, derivWithin]
   change
-    ((ContinuousMultilinearMap.mkPiField 𝕜 (Fin n)
+    ((ContinuousMultilinearMap.mkPiRing 𝕜 (Fin n)
             ((fderivWithin 𝕜 (iteratedDerivWithin n f s) s x : 𝕜 → F) 1) :
           (Fin n → 𝕜) → F)
         fun i : Fin n => 1) =

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

@@ -110,7 +110,7 @@ theorem iteratedFDerivWithin_eq_equiv_comp :
       ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDerivWithin n f s :=
   by
   rw [iteratedDerivWithin_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
-    Function.left_id]
+    Function.id_comp]
 #align iterated_fderiv_within_eq_equiv_comp iteratedFDerivWithin_eq_equiv_comp
 -/
 
@@ -288,7 +288,7 @@ theorem iteratedFDeriv_eq_equiv_comp :
     iteratedFDeriv 𝕜 n f = ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDeriv n f :=
   by
   rw [iteratedDeriv_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
-    Function.left_id]
+    Function.id_comp]
 #align iterated_fderiv_eq_equiv_comp iteratedFDeriv_eq_equiv_comp
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Analysis.Calculus.Deriv.Comp
-import Mathbin.Analysis.Calculus.ContDiffDef
+import Analysis.Calculus.Deriv.Comp
+import Analysis.Calculus.ContDiffDef
 
 #align_import analysis.calculus.iterated_deriv from "leanprover-community/mathlib"@"2ebc1d6c2fed9f54c95bbc3998eaa5570527129a"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! leanprover-community/mathlib commit 2ebc1d6c2fed9f54c95bbc3998eaa5570527129a
-! 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.ContDiffDef
 
+#align_import analysis.calculus.iterated_deriv from "leanprover-community/mathlib"@"2ebc1d6c2fed9f54c95bbc3998eaa5570527129a"
+
 /-!
 # One-dimensional iterated derivatives
 

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

@@ -78,19 +78,24 @@ def iteratedDerivWithin (n : ℕ) (f : 𝕜 → F) (s : Set 𝕜) (x : 𝕜) : F
 
 variable {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜}
 
+#print iteratedDerivWithin_univ /-
 theorem iteratedDerivWithin_univ : iteratedDerivWithin n f univ = iteratedDeriv n f := by ext x;
   rw [iteratedDerivWithin, iteratedDeriv, iteratedFDerivWithin_univ]
 #align iterated_deriv_within_univ iteratedDerivWithin_univ
+-/
 
 /-! ### Properties of the iterated derivative within a set -/
 
 
+#print iteratedDerivWithin_eq_iteratedFDerivWithin /-
 theorem iteratedDerivWithin_eq_iteratedFDerivWithin :
     iteratedDerivWithin n f s x =
       (iteratedFDerivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) fun i : Fin n => 1 :=
   rfl
 #align iterated_deriv_within_eq_iterated_fderiv_within iteratedDerivWithin_eq_iteratedFDerivWithin
+-/
 
+#print iteratedDerivWithin_eq_equiv_comp /-
 /-- Write the iterated derivative as the composition of a continuous linear equiv and the iterated
 Fréchet derivative -/
 theorem iteratedDerivWithin_eq_equiv_comp :
@@ -98,7 +103,9 @@ theorem iteratedDerivWithin_eq_equiv_comp :
       (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFDerivWithin 𝕜 n f s :=
   by ext x; rfl
 #align iterated_deriv_within_eq_equiv_comp iteratedDerivWithin_eq_equiv_comp
+-/
 
+#print iteratedFDerivWithin_eq_equiv_comp /-
 /-- Write the iterated Fréchet derivative as the composition of a continuous linear equiv and the
 iterated derivative. -/
 theorem iteratedFDerivWithin_eq_equiv_comp :
@@ -108,6 +115,7 @@ theorem iteratedFDerivWithin_eq_equiv_comp :
   rw [iteratedDerivWithin_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
     Function.left_id]
 #align iterated_fderiv_within_eq_equiv_comp iteratedFDerivWithin_eq_equiv_comp
+-/
 
 #print iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod /-
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
@@ -128,17 +136,22 @@ theorem norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin :
 #align norm_iterated_fderiv_within_eq_norm_iterated_deriv_within norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin
 -/
 
+#print iteratedDerivWithin_zero /-
 @[simp]
 theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f := by ext x;
   simp [iteratedDerivWithin]
 #align iterated_deriv_within_zero iteratedDerivWithin_zero
+-/
 
+#print iteratedDerivWithin_one /-
 @[simp]
 theorem iteratedDerivWithin_one {x : 𝕜} (h : UniqueDiffWithinAt 𝕜 s x) :
     iteratedDerivWithin 1 f s x = derivWithin f s x := by
   simp only [iteratedDerivWithin, iteratedFDerivWithin_one_apply h]; rfl
 #align iterated_deriv_within_one iteratedDerivWithin_one
+-/
 
+#print contDiffOn_of_continuousOn_differentiableOn_deriv /-
 /-- If the first `n` derivatives within a set of a function are continuous, and its first `n-1`
 derivatives are differentiable, then the function is `C^n`. This is not an equivalence in general,
 but this is an equivalence when the set has unique derivatives, see
@@ -152,7 +165,9 @@ theorem contDiffOn_of_continuousOn_differentiableOn_deriv {n : ℕ∞}
   · simpa [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_continuousOn_iff]
   · simpa [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]
 #align cont_diff_on_of_continuous_on_differentiable_on_deriv contDiffOn_of_continuousOn_differentiableOn_deriv
+-/
 
+#print contDiffOn_of_differentiableOn_deriv /-
 /-- To check that a function is `n` times continuously differentiable, it suffices to check that its
 first `n` derivatives are differentiable. This is slightly too strong as the condition we
 require on the `n`-th derivative is differentiability instead of continuity, but it has the
@@ -164,7 +179,9 @@ theorem contDiffOn_of_differentiableOn_deriv {n : ℕ∞}
   apply contDiffOn_of_differentiableOn
   simpa only [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]
 #align cont_diff_on_of_differentiable_on_deriv contDiffOn_of_differentiableOn_deriv
+-/
 
+#print ContDiffOn.continuousOn_iteratedDerivWithin /-
 /-- On a set with unique derivatives, a `C^n` function has derivatives up to `n` which are
 continuous. -/
 theorem ContDiffOn.continuousOn_iteratedDerivWithin {n : ℕ∞} {m : ℕ} (h : ContDiffOn 𝕜 n f s)
@@ -172,7 +189,9 @@ theorem ContDiffOn.continuousOn_iteratedDerivWithin {n : ℕ∞} {m : ℕ} (h :
   simpa only [iteratedDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_continuousOn_iff] using
     h.continuous_on_iterated_fderiv_within hmn hs
 #align cont_diff_on.continuous_on_iterated_deriv_within ContDiffOn.continuousOn_iteratedDerivWithin
+-/
 
+#print ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin /-
 theorem ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin {n : ℕ∞} {m : ℕ}
     (h : ContDiffWithinAt 𝕜 n f s x) (hmn : (m : ℕ∞) < n) (hs : UniqueDiffOn 𝕜 (insert x s)) :
     DifferentiableWithinAt 𝕜 (iteratedDerivWithin m f s) s x := by
@@ -180,7 +199,9 @@ theorem ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin {n : ℕ∞}
     LinearIsometryEquiv.comp_differentiableWithinAt_iff] using
     h.differentiable_within_at_iterated_fderiv_within hmn hs
 #align cont_diff_within_at.differentiable_within_at_iterated_deriv_within ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin
+-/
 
+#print ContDiffOn.differentiableOn_iteratedDerivWithin /-
 /-- On a set with unique derivatives, a `C^n` function has derivatives less than `n` which are
 differentiable. -/
 theorem ContDiffOn.differentiableOn_iteratedDerivWithin {n : ℕ∞} {m : ℕ} (h : ContDiffOn 𝕜 n f s)
@@ -188,7 +209,9 @@ theorem ContDiffOn.differentiableOn_iteratedDerivWithin {n : ℕ∞} {m : ℕ} (
     DifferentiableOn 𝕜 (iteratedDerivWithin m f s) s := fun x hx =>
   (h x hx).differentiableWithinAt_iteratedDerivWithin hmn <| by rwa [insert_eq_of_mem hx]
 #align cont_diff_on.differentiable_on_iterated_deriv_within ContDiffOn.differentiableOn_iteratedDerivWithin
+-/
 
+#print contDiffOn_iff_continuousOn_differentiableOn_deriv /-
 /-- The property of being `C^n`, initially defined in terms of the Fréchet derivative, can be
 reformulated in terms of the one-dimensional derivative on sets with unique derivatives. -/
 theorem contDiffOn_iff_continuousOn_differentiableOn_deriv {n : ℕ∞} (hs : UniqueDiffOn 𝕜 s) :
@@ -199,7 +222,9 @@ theorem contDiffOn_iff_continuousOn_differentiableOn_deriv {n : ℕ∞} (hs : Un
   simp only [contDiffOn_iff_continuousOn_differentiableOn hs, iteratedFDerivWithin_eq_equiv_comp,
     LinearIsometryEquiv.comp_continuousOn_iff, LinearIsometryEquiv.comp_differentiableOn_iff]
 #align cont_diff_on_iff_continuous_on_differentiable_on_deriv contDiffOn_iff_continuousOn_differentiableOn_deriv
+-/
 
+#print iteratedDerivWithin_succ /-
 /-- The `n+1`-th iterated derivative within a set with unique derivatives can be obtained by
 differentiating the `n`-th iterated derivative. -/
 theorem iteratedDerivWithin_succ {x : 𝕜} (hxs : UniqueDiffWithinAt 𝕜 s x) :
@@ -215,7 +240,9 @@ theorem iteratedDerivWithin_succ {x : 𝕜} (hxs : UniqueDiffWithinAt 𝕜 s x)
       (fderivWithin 𝕜 (iteratedDerivWithin n f s) s x : 𝕜 → F) 1
   simp
 #align iterated_deriv_within_succ iteratedDerivWithin_succ
+-/
 
+#print iteratedDerivWithin_eq_iterate /-
 /-- The `n`-th iterated derivative within a set with unique derivatives can be obtained by
 iterating `n` times the differentiation operation. -/
 theorem iteratedDerivWithin_eq_iterate {x : 𝕜} (hs : UniqueDiffOn 𝕜 s) (hx : x ∈ s) :
@@ -226,22 +253,28 @@ theorem iteratedDerivWithin_eq_iterate {x : 𝕜} (hs : UniqueDiffOn 𝕜 s) (hx
   · rw [iteratedDerivWithin_succ (hs x hx), Function.iterate_succ']
     exact derivWithin_congr (fun y hy => IH hy) (IH hx)
 #align iterated_deriv_within_eq_iterate iteratedDerivWithin_eq_iterate
+-/
 
+#print iteratedDerivWithin_succ' /-
 /-- The `n+1`-th iterated derivative within a set with unique derivatives can be obtained by
 taking the `n`-th derivative of the derivative. -/
 theorem iteratedDerivWithin_succ' {x : 𝕜} (hxs : UniqueDiffOn 𝕜 s) (hx : x ∈ s) :
     iteratedDerivWithin (n + 1) f s x = (iteratedDerivWithin n (derivWithin f s) s) x := by
   rw [iteratedDerivWithin_eq_iterate hxs hx, iteratedDerivWithin_eq_iterate hxs hx]; rfl
 #align iterated_deriv_within_succ' iteratedDerivWithin_succ'
+-/
 
 /-! ### Properties of the iterated derivative on the whole space -/
 
 
+#print iteratedDeriv_eq_iteratedFDeriv /-
 theorem iteratedDeriv_eq_iteratedFDeriv :
     iteratedDeriv n f x = (iteratedFDeriv 𝕜 n f x : (Fin n → 𝕜) → F) fun i : Fin n => 1 :=
   rfl
 #align iterated_deriv_eq_iterated_fderiv iteratedDeriv_eq_iteratedFDeriv
+-/
 
+#print iteratedDeriv_eq_equiv_comp /-
 /-- Write the iterated derivative as the composition of a continuous linear equiv and the iterated
 Fréchet derivative -/
 theorem iteratedDeriv_eq_equiv_comp :
@@ -249,7 +282,9 @@ theorem iteratedDeriv_eq_equiv_comp :
       (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFDeriv 𝕜 n f :=
   by ext x; rfl
 #align iterated_deriv_eq_equiv_comp iteratedDeriv_eq_equiv_comp
+-/
 
+#print iteratedFDeriv_eq_equiv_comp /-
 /-- Write the iterated Fréchet derivative as the composition of a continuous linear equiv and the
 iterated derivative. -/
 theorem iteratedFDeriv_eq_equiv_comp :
@@ -258,6 +293,7 @@ theorem iteratedFDeriv_eq_equiv_comp :
   rw [iteratedDeriv_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
     Function.left_id]
 #align iterated_fderiv_eq_equiv_comp iteratedFDeriv_eq_equiv_comp
+-/
 
 #print iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod /-
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
@@ -275,14 +311,19 @@ theorem norm_iteratedFDeriv_eq_norm_iteratedDeriv :
 #align norm_iterated_fderiv_eq_norm_iterated_deriv norm_iteratedFDeriv_eq_norm_iteratedDeriv
 -/
 
+#print iteratedDeriv_zero /-
 @[simp]
 theorem iteratedDeriv_zero : iteratedDeriv 0 f = f := by ext x; simp [iteratedDeriv]
 #align iterated_deriv_zero iteratedDeriv_zero
+-/
 
+#print iteratedDeriv_one /-
 @[simp]
 theorem iteratedDeriv_one : iteratedDeriv 1 f = deriv f := by ext x; simp [iteratedDeriv]; rfl
 #align iterated_deriv_one iteratedDeriv_one
+-/
 
+#print contDiff_iff_iteratedDeriv /-
 /-- The property of being `C^n`, initially defined in terms of the Fréchet derivative, can be
 reformulated in terms of the one-dimensional derivative. -/
 theorem contDiff_iff_iteratedDeriv {n : ℕ∞} :
@@ -293,7 +334,9 @@ theorem contDiff_iff_iteratedDeriv {n : ℕ∞} :
   simp only [contDiff_iff_continuous_differentiable, iteratedFDeriv_eq_equiv_comp,
     LinearIsometryEquiv.comp_continuous_iff, LinearIsometryEquiv.comp_differentiable_iff]
 #align cont_diff_iff_iterated_deriv contDiff_iff_iteratedDeriv
+-/
 
+#print contDiff_of_differentiable_iteratedDeriv /-
 /-- To check that a function is `n` times continuously differentiable, it suffices to check that its
 first `n` derivatives are differentiable. This is slightly too strong as the condition we
 require on the `n`-th derivative is differentiability instead of continuity, but it has the
@@ -303,17 +346,23 @@ theorem contDiff_of_differentiable_iteratedDeriv {n : ℕ∞}
     (h : ∀ m : ℕ, (m : ℕ∞) ≤ n → Differentiable 𝕜 (iteratedDeriv m f)) : ContDiff 𝕜 n f :=
   contDiff_iff_iteratedDeriv.2 ⟨fun m hm => (h m hm).Continuous, fun m hm => h m (le_of_lt hm)⟩
 #align cont_diff_of_differentiable_iterated_deriv contDiff_of_differentiable_iteratedDeriv
+-/
 
+#print ContDiff.continuous_iteratedDeriv /-
 theorem ContDiff.continuous_iteratedDeriv {n : ℕ∞} (m : ℕ) (h : ContDiff 𝕜 n f)
     (hmn : (m : ℕ∞) ≤ n) : Continuous (iteratedDeriv m f) :=
   (contDiff_iff_iteratedDeriv.1 h).1 m hmn
 #align cont_diff.continuous_iterated_deriv ContDiff.continuous_iteratedDeriv
+-/
 
+#print ContDiff.differentiable_iteratedDeriv /-
 theorem ContDiff.differentiable_iteratedDeriv {n : ℕ∞} (m : ℕ) (h : ContDiff 𝕜 n f)
     (hmn : (m : ℕ∞) < n) : Differentiable 𝕜 (iteratedDeriv m f) :=
   (contDiff_iff_iteratedDeriv.1 h).2 m hmn
 #align cont_diff.differentiable_iterated_deriv ContDiff.differentiable_iteratedDeriv
+-/
 
+#print iteratedDeriv_succ /-
 /-- The `n+1`-th iterated derivative can be obtained by differentiating the `n`-th
 iterated derivative. -/
 theorem iteratedDeriv_succ : iteratedDeriv (n + 1) f = deriv (iteratedDeriv n f) :=
@@ -322,7 +371,9 @@ theorem iteratedDeriv_succ : iteratedDeriv (n + 1) f = deriv (iteratedDeriv n f)
   rw [← iteratedDerivWithin_univ, ← iteratedDerivWithin_univ, ← derivWithin_univ]
   exact iteratedDerivWithin_succ uniqueDiffWithinAt_univ
 #align iterated_deriv_succ iteratedDeriv_succ
+-/
 
+#print iteratedDeriv_eq_iterate /-
 /-- The `n`-th iterated derivative can be obtained by iterating `n` times the
 differentiation operation. -/
 theorem iteratedDeriv_eq_iterate : iteratedDeriv n f = (deriv^[n]) f :=
@@ -332,10 +383,13 @@ theorem iteratedDeriv_eq_iterate : iteratedDeriv n f = (deriv^[n]) f :=
   convert iteratedDerivWithin_eq_iterate uniqueDiffOn_univ (mem_univ x)
   simp [derivWithin_univ]
 #align iterated_deriv_eq_iterate iteratedDeriv_eq_iterate
+-/
 
+#print iteratedDeriv_succ' /-
 /-- The `n+1`-th iterated derivative can be obtained by taking the `n`-th derivative of the
 derivative. -/
 theorem iteratedDeriv_succ' : iteratedDeriv (n + 1) f = iteratedDeriv n (deriv f) := by
   rw [iteratedDeriv_eq_iterate, iteratedDeriv_eq_iterate]; rfl
 #align iterated_deriv_succ' iteratedDeriv_succ'
+-/
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
+! leanprover-community/mathlib commit 2ebc1d6c2fed9f54c95bbc3998eaa5570527129a
 ! 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.ContDiffDef
 /-!
 # One-dimensional iterated derivatives
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the `n`-th derivative of a function `f : 𝕜 → F` as a function
 `iterated_deriv n f : 𝕜 → F`, as well as a version on domains `iterated_deriv_within n f s : 𝕜 → F`,
 and prove their basic properties.

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

@@ -58,16 +58,20 @@ variable {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
+#print iteratedDeriv /-
 /-- The `n`-th iterated derivative of a function from `𝕜` to `F`, as a function from `𝕜` to `F`. -/
 def iteratedDeriv (n : ℕ) (f : 𝕜 → F) (x : 𝕜) : F :=
   (iteratedFDeriv 𝕜 n f x : (Fin n → 𝕜) → F) fun i : Fin n => 1
 #align iterated_deriv iteratedDeriv
+-/
 
+#print iteratedDerivWithin /-
 /-- The `n`-th iterated derivative of a function from `𝕜` to `F` within a set `s`, as a function
 from `𝕜` to `F`. -/
 def iteratedDerivWithin (n : ℕ) (f : 𝕜 → F) (s : Set 𝕜) (x : 𝕜) : F :=
   (iteratedFDerivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) fun i : Fin n => 1
 #align iterated_deriv_within iteratedDerivWithin
+-/
 
 variable {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜}
 
@@ -102,6 +106,7 @@ theorem iteratedFDerivWithin_eq_equiv_comp :
     Function.left_id]
 #align iterated_fderiv_within_eq_equiv_comp iteratedFDerivWithin_eq_equiv_comp
 
+#print iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod /-
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
 multiplied by the product of the `m i`s. -/
 theorem iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod {m : Fin n → 𝕜} :
@@ -111,11 +116,14 @@ theorem iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod {m : Fin n 
   rw [iteratedDerivWithin_eq_iteratedFDerivWithin, ← ContinuousMultilinearMap.map_smul_univ]
   simp
 #align iterated_fderiv_within_apply_eq_iterated_deriv_within_mul_prod iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod
+-/
 
+#print norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin /-
 theorem norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin :
     ‖iteratedFDerivWithin 𝕜 n f s x‖ = ‖iteratedDerivWithin n f s x‖ := by
   rw [iteratedDerivWithin_eq_equiv_comp, LinearIsometryEquiv.norm_map]
 #align norm_iterated_fderiv_within_eq_norm_iterated_deriv_within norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin
+-/
 
 @[simp]
 theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f := by ext x;
@@ -248,17 +256,21 @@ theorem iteratedFDeriv_eq_equiv_comp :
     Function.left_id]
 #align iterated_fderiv_eq_equiv_comp iteratedFDeriv_eq_equiv_comp
 
+#print iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod /-
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
 multiplied by the product of the `m i`s. -/
 theorem iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod {m : Fin n → 𝕜} :
     (iteratedFDeriv 𝕜 n f x : (Fin n → 𝕜) → F) m = (∏ i, m i) • iteratedDeriv n f x := by
   rw [iteratedDeriv_eq_iteratedFDeriv, ← ContinuousMultilinearMap.map_smul_univ]; simp
 #align iterated_fderiv_apply_eq_iterated_deriv_mul_prod iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod
+-/
 
+#print norm_iteratedFDeriv_eq_norm_iteratedDeriv /-
 theorem norm_iteratedFDeriv_eq_norm_iteratedDeriv :
     ‖iteratedFDeriv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖ := by
   rw [iteratedDeriv_eq_equiv_comp, LinearIsometryEquiv.norm_map]
 #align norm_iterated_fderiv_eq_norm_iterated_deriv norm_iteratedFDeriv_eq_norm_iteratedDeriv
+-/
 
 @[simp]
 theorem iteratedDeriv_zero : iteratedDeriv 0 f = f := by ext x; simp [iteratedDeriv]

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

@@ -60,62 +60,62 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
 /-- The `n`-th iterated derivative of a function from `𝕜` to `F`, as a function from `𝕜` to `F`. -/
 def iteratedDeriv (n : ℕ) (f : 𝕜 → F) (x : 𝕜) : F :=
-  (iteratedFderiv 𝕜 n f x : (Fin n → 𝕜) → F) fun i : Fin n => 1
+  (iteratedFDeriv 𝕜 n f x : (Fin n → 𝕜) → F) fun i : Fin n => 1
 #align iterated_deriv iteratedDeriv
 
 /-- The `n`-th iterated derivative of a function from `𝕜` to `F` within a set `s`, as a function
 from `𝕜` to `F`. -/
 def iteratedDerivWithin (n : ℕ) (f : 𝕜 → F) (s : Set 𝕜) (x : 𝕜) : F :=
-  (iteratedFderivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) fun i : Fin n => 1
+  (iteratedFDerivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) fun i : Fin n => 1
 #align iterated_deriv_within iteratedDerivWithin
 
 variable {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜}
 
 theorem iteratedDerivWithin_univ : iteratedDerivWithin n f univ = iteratedDeriv n f := by ext x;
-  rw [iteratedDerivWithin, iteratedDeriv, iteratedFderivWithin_univ]
+  rw [iteratedDerivWithin, iteratedDeriv, iteratedFDerivWithin_univ]
 #align iterated_deriv_within_univ iteratedDerivWithin_univ
 
 /-! ### Properties of the iterated derivative within a set -/
 
 
-theorem iteratedDerivWithin_eq_iteratedFderivWithin :
+theorem iteratedDerivWithin_eq_iteratedFDerivWithin :
     iteratedDerivWithin n f s x =
-      (iteratedFderivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) fun i : Fin n => 1 :=
+      (iteratedFDerivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) fun i : Fin n => 1 :=
   rfl
-#align iterated_deriv_within_eq_iterated_fderiv_within iteratedDerivWithin_eq_iteratedFderivWithin
+#align iterated_deriv_within_eq_iterated_fderiv_within iteratedDerivWithin_eq_iteratedFDerivWithin
 
 /-- Write the iterated derivative as the composition of a continuous linear equiv and the iterated
 Fréchet derivative -/
 theorem iteratedDerivWithin_eq_equiv_comp :
     iteratedDerivWithin n f s =
-      (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFderivWithin 𝕜 n f s :=
+      (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFDerivWithin 𝕜 n f s :=
   by ext x; rfl
 #align iterated_deriv_within_eq_equiv_comp iteratedDerivWithin_eq_equiv_comp
 
 /-- Write the iterated Fréchet derivative as the composition of a continuous linear equiv and the
 iterated derivative. -/
-theorem iteratedFderivWithin_eq_equiv_comp :
-    iteratedFderivWithin 𝕜 n f s =
+theorem iteratedFDerivWithin_eq_equiv_comp :
+    iteratedFDerivWithin 𝕜 n f s =
       ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDerivWithin n f s :=
   by
   rw [iteratedDerivWithin_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
     Function.left_id]
-#align iterated_fderiv_within_eq_equiv_comp iteratedFderivWithin_eq_equiv_comp
+#align iterated_fderiv_within_eq_equiv_comp iteratedFDerivWithin_eq_equiv_comp
 
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
 multiplied by the product of the `m i`s. -/
-theorem iteratedFderivWithin_apply_eq_iteratedDerivWithin_mul_prod {m : Fin n → 𝕜} :
-    (iteratedFderivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) m =
+theorem iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod {m : Fin n → 𝕜} :
+    (iteratedFDerivWithin 𝕜 n f s x : (Fin n → 𝕜) → F) m =
       (∏ i, m i) • iteratedDerivWithin n f s x :=
   by
-  rw [iteratedDerivWithin_eq_iteratedFderivWithin, ← ContinuousMultilinearMap.map_smul_univ]
+  rw [iteratedDerivWithin_eq_iteratedFDerivWithin, ← ContinuousMultilinearMap.map_smul_univ]
   simp
-#align iterated_fderiv_within_apply_eq_iterated_deriv_within_mul_prod iteratedFderivWithin_apply_eq_iteratedDerivWithin_mul_prod
+#align iterated_fderiv_within_apply_eq_iterated_deriv_within_mul_prod iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod
 
-theorem norm_iteratedFderivWithin_eq_norm_iteratedDerivWithin :
-    ‖iteratedFderivWithin 𝕜 n f s x‖ = ‖iteratedDerivWithin n f s x‖ := by
+theorem norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin :
+    ‖iteratedFDerivWithin 𝕜 n f s x‖ = ‖iteratedDerivWithin n f s x‖ := by
   rw [iteratedDerivWithin_eq_equiv_comp, LinearIsometryEquiv.norm_map]
-#align norm_iterated_fderiv_within_eq_norm_iterated_deriv_within norm_iteratedFderivWithin_eq_norm_iteratedDerivWithin
+#align norm_iterated_fderiv_within_eq_norm_iterated_deriv_within norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin
 
 @[simp]
 theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f := by ext x;
@@ -125,7 +125,7 @@ theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f := by ext x;
 @[simp]
 theorem iteratedDerivWithin_one {x : 𝕜} (h : UniqueDiffWithinAt 𝕜 s x) :
     iteratedDerivWithin 1 f s x = derivWithin f s x := by
-  simp only [iteratedDerivWithin, iteratedFderivWithin_one_apply h]; rfl
+  simp only [iteratedDerivWithin, iteratedFDerivWithin_one_apply h]; rfl
 #align iterated_deriv_within_one iteratedDerivWithin_one
 
 /-- If the first `n` derivatives within a set of a function are continuous, and its first `n-1`
@@ -138,8 +138,8 @@ theorem contDiffOn_of_continuousOn_differentiableOn_deriv {n : ℕ∞}
     ContDiffOn 𝕜 n f s :=
   by
   apply contDiffOn_of_continuousOn_differentiableOn
-  · simpa [iteratedFderivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_continuousOn_iff]
-  · simpa [iteratedFderivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]
+  · simpa [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_continuousOn_iff]
+  · simpa [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]
 #align cont_diff_on_of_continuous_on_differentiable_on_deriv contDiffOn_of_continuousOn_differentiableOn_deriv
 
 /-- To check that a function is `n` times continuously differentiable, it suffices to check that its
@@ -151,7 +151,7 @@ theorem contDiffOn_of_differentiableOn_deriv {n : ℕ∞}
     (h : ∀ m : ℕ, (m : ℕ∞) ≤ n → DifferentiableOn 𝕜 (iteratedDerivWithin m f s) s) :
     ContDiffOn 𝕜 n f s := by
   apply contDiffOn_of_differentiableOn
-  simpa only [iteratedFderivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]
+  simpa only [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]
 #align cont_diff_on_of_differentiable_on_deriv contDiffOn_of_differentiableOn_deriv
 
 /-- On a set with unique derivatives, a `C^n` function has derivatives up to `n` which are
@@ -185,7 +185,7 @@ theorem contDiffOn_iff_continuousOn_differentiableOn_deriv {n : ℕ∞} (hs : Un
       (∀ m : ℕ, (m : ℕ∞) ≤ n → ContinuousOn (iteratedDerivWithin m f s) s) ∧
         ∀ m : ℕ, (m : ℕ∞) < n → DifferentiableOn 𝕜 (iteratedDerivWithin m f s) s :=
   by
-  simp only [contDiffOn_iff_continuousOn_differentiableOn hs, iteratedFderivWithin_eq_equiv_comp,
+  simp only [contDiffOn_iff_continuousOn_differentiableOn hs, iteratedFDerivWithin_eq_equiv_comp,
     LinearIsometryEquiv.comp_continuousOn_iff, LinearIsometryEquiv.comp_differentiableOn_iff]
 #align cont_diff_on_iff_continuous_on_differentiable_on_deriv contDiffOn_iff_continuousOn_differentiableOn_deriv
 
@@ -194,8 +194,8 @@ differentiating the `n`-th iterated derivative. -/
 theorem iteratedDerivWithin_succ {x : 𝕜} (hxs : UniqueDiffWithinAt 𝕜 s x) :
     iteratedDerivWithin (n + 1) f s x = derivWithin (iteratedDerivWithin n f s) s x :=
   by
-  rw [iteratedDerivWithin_eq_iteratedFderivWithin, iteratedFderivWithin_succ_apply_left,
-    iteratedFderivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_fderivWithin _ hxs, derivWithin]
+  rw [iteratedDerivWithin_eq_iteratedFDerivWithin, iteratedFDerivWithin_succ_apply_left,
+    iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_fderivWithin _ hxs, derivWithin]
   change
     ((ContinuousMultilinearMap.mkPiField 𝕜 (Fin n)
             ((fderivWithin 𝕜 (iteratedDerivWithin n f s) s x : 𝕜 → F) 1) :
@@ -226,39 +226,39 @@ theorem iteratedDerivWithin_succ' {x : 𝕜} (hxs : UniqueDiffOn 𝕜 s) (hx : x
 /-! ### Properties of the iterated derivative on the whole space -/
 
 
-theorem iteratedDeriv_eq_iteratedFderiv :
-    iteratedDeriv n f x = (iteratedFderiv 𝕜 n f x : (Fin n → 𝕜) → F) fun i : Fin n => 1 :=
+theorem iteratedDeriv_eq_iteratedFDeriv :
+    iteratedDeriv n f x = (iteratedFDeriv 𝕜 n f x : (Fin n → 𝕜) → F) fun i : Fin n => 1 :=
   rfl
-#align iterated_deriv_eq_iterated_fderiv iteratedDeriv_eq_iteratedFderiv
+#align iterated_deriv_eq_iterated_fderiv iteratedDeriv_eq_iteratedFDeriv
 
 /-- Write the iterated derivative as the composition of a continuous linear equiv and the iterated
 Fréchet derivative -/
 theorem iteratedDeriv_eq_equiv_comp :
     iteratedDeriv n f =
-      (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFderiv 𝕜 n f :=
+      (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFDeriv 𝕜 n f :=
   by ext x; rfl
 #align iterated_deriv_eq_equiv_comp iteratedDeriv_eq_equiv_comp
 
 /-- Write the iterated Fréchet derivative as the composition of a continuous linear equiv and the
 iterated derivative. -/
-theorem iteratedFderiv_eq_equiv_comp :
-    iteratedFderiv 𝕜 n f = ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDeriv n f :=
+theorem iteratedFDeriv_eq_equiv_comp :
+    iteratedFDeriv 𝕜 n f = ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDeriv n f :=
   by
   rw [iteratedDeriv_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
     Function.left_id]
-#align iterated_fderiv_eq_equiv_comp iteratedFderiv_eq_equiv_comp
+#align iterated_fderiv_eq_equiv_comp iteratedFDeriv_eq_equiv_comp
 
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
 multiplied by the product of the `m i`s. -/
-theorem iteratedFderiv_apply_eq_iteratedDeriv_mul_prod {m : Fin n → 𝕜} :
-    (iteratedFderiv 𝕜 n f x : (Fin n → 𝕜) → F) m = (∏ i, m i) • iteratedDeriv n f x := by
-  rw [iteratedDeriv_eq_iteratedFderiv, ← ContinuousMultilinearMap.map_smul_univ]; simp
-#align iterated_fderiv_apply_eq_iterated_deriv_mul_prod iteratedFderiv_apply_eq_iteratedDeriv_mul_prod
+theorem iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod {m : Fin n → 𝕜} :
+    (iteratedFDeriv 𝕜 n f x : (Fin n → 𝕜) → F) m = (∏ i, m i) • iteratedDeriv n f x := by
+  rw [iteratedDeriv_eq_iteratedFDeriv, ← ContinuousMultilinearMap.map_smul_univ]; simp
+#align iterated_fderiv_apply_eq_iterated_deriv_mul_prod iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod
 
-theorem norm_iteratedFderiv_eq_norm_iteratedDeriv :
-    ‖iteratedFderiv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖ := by
+theorem norm_iteratedFDeriv_eq_norm_iteratedDeriv :
+    ‖iteratedFDeriv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖ := by
   rw [iteratedDeriv_eq_equiv_comp, LinearIsometryEquiv.norm_map]
-#align norm_iterated_fderiv_eq_norm_iterated_deriv norm_iteratedFderiv_eq_norm_iteratedDeriv
+#align norm_iterated_fderiv_eq_norm_iterated_deriv norm_iteratedFDeriv_eq_norm_iteratedDeriv
 
 @[simp]
 theorem iteratedDeriv_zero : iteratedDeriv 0 f = f := by ext x; simp [iteratedDeriv]
@@ -275,7 +275,7 @@ theorem contDiff_iff_iteratedDeriv {n : ℕ∞} :
       (∀ m : ℕ, (m : ℕ∞) ≤ n → Continuous (iteratedDeriv m f)) ∧
         ∀ m : ℕ, (m : ℕ∞) < n → Differentiable 𝕜 (iteratedDeriv m f) :=
   by
-  simp only [contDiff_iff_continuous_differentiable, iteratedFderiv_eq_equiv_comp,
+  simp only [contDiff_iff_continuous_differentiable, iteratedFDeriv_eq_equiv_comp,
     LinearIsometryEquiv.comp_continuous_iff, LinearIsometryEquiv.comp_differentiable_iff]
 #align cont_diff_iff_iterated_deriv contDiff_iff_iteratedDeriv
 

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

@@ -48,7 +48,7 @@ iterated Fréchet derivative.
 
 noncomputable section
 
-open Classical Topology BigOperators
+open scoped Classical Topology BigOperators
 
 open Filter Asymptotics Set
 

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

@@ -71,9 +71,7 @@ def iteratedDerivWithin (n : ℕ) (f : 𝕜 → F) (s : Set 𝕜) (x : 𝕜) : F
 
 variable {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜}
 
-theorem iteratedDerivWithin_univ : iteratedDerivWithin n f univ = iteratedDeriv n f :=
-  by
-  ext x
+theorem iteratedDerivWithin_univ : iteratedDerivWithin n f univ = iteratedDeriv n f := by ext x;
   rw [iteratedDerivWithin, iteratedDeriv, iteratedFderivWithin_univ]
 #align iterated_deriv_within_univ iteratedDerivWithin_univ
 
@@ -91,9 +89,7 @@ Fréchet derivative -/
 theorem iteratedDerivWithin_eq_equiv_comp :
     iteratedDerivWithin n f s =
       (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFderivWithin 𝕜 n f s :=
-  by
-  ext x
-  rfl
+  by ext x; rfl
 #align iterated_deriv_within_eq_equiv_comp iteratedDerivWithin_eq_equiv_comp
 
 /-- Write the iterated Fréchet derivative as the composition of a continuous linear equiv and the
@@ -122,18 +118,14 @@ theorem norm_iteratedFderivWithin_eq_norm_iteratedDerivWithin :
 #align norm_iterated_fderiv_within_eq_norm_iterated_deriv_within norm_iteratedFderivWithin_eq_norm_iteratedDerivWithin
 
 @[simp]
-theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f :=
-  by
-  ext x
+theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f := by ext x;
   simp [iteratedDerivWithin]
 #align iterated_deriv_within_zero iteratedDerivWithin_zero
 
 @[simp]
 theorem iteratedDerivWithin_one {x : 𝕜} (h : UniqueDiffWithinAt 𝕜 s x) :
-    iteratedDerivWithin 1 f s x = derivWithin f s x :=
-  by
-  simp only [iteratedDerivWithin, iteratedFderivWithin_one_apply h]
-  rfl
+    iteratedDerivWithin 1 f s x = derivWithin f s x := by
+  simp only [iteratedDerivWithin, iteratedFderivWithin_one_apply h]; rfl
 #align iterated_deriv_within_one iteratedDerivWithin_one
 
 /-- If the first `n` derivatives within a set of a function are continuous, and its first `n-1`
@@ -227,10 +219,8 @@ theorem iteratedDerivWithin_eq_iterate {x : 𝕜} (hs : UniqueDiffOn 𝕜 s) (hx
 /-- The `n+1`-th iterated derivative within a set with unique derivatives can be obtained by
 taking the `n`-th derivative of the derivative. -/
 theorem iteratedDerivWithin_succ' {x : 𝕜} (hxs : UniqueDiffOn 𝕜 s) (hx : x ∈ s) :
-    iteratedDerivWithin (n + 1) f s x = (iteratedDerivWithin n (derivWithin f s) s) x :=
-  by
-  rw [iteratedDerivWithin_eq_iterate hxs hx, iteratedDerivWithin_eq_iterate hxs hx]
-  rfl
+    iteratedDerivWithin (n + 1) f s x = (iteratedDerivWithin n (derivWithin f s) s) x := by
+  rw [iteratedDerivWithin_eq_iterate hxs hx, iteratedDerivWithin_eq_iterate hxs hx]; rfl
 #align iterated_deriv_within_succ' iteratedDerivWithin_succ'
 
 /-! ### Properties of the iterated derivative on the whole space -/
@@ -246,9 +236,7 @@ Fréchet derivative -/
 theorem iteratedDeriv_eq_equiv_comp :
     iteratedDeriv n f =
       (ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFderiv 𝕜 n f :=
-  by
-  ext x
-  rfl
+  by ext x; rfl
 #align iterated_deriv_eq_equiv_comp iteratedDeriv_eq_equiv_comp
 
 /-- Write the iterated Fréchet derivative as the composition of a continuous linear equiv and the
@@ -263,10 +251,8 @@ theorem iteratedFderiv_eq_equiv_comp :
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
 multiplied by the product of the `m i`s. -/
 theorem iteratedFderiv_apply_eq_iteratedDeriv_mul_prod {m : Fin n → 𝕜} :
-    (iteratedFderiv 𝕜 n f x : (Fin n → 𝕜) → F) m = (∏ i, m i) • iteratedDeriv n f x :=
-  by
-  rw [iteratedDeriv_eq_iteratedFderiv, ← ContinuousMultilinearMap.map_smul_univ]
-  simp
+    (iteratedFderiv 𝕜 n f x : (Fin n → 𝕜) → F) m = (∏ i, m i) • iteratedDeriv n f x := by
+  rw [iteratedDeriv_eq_iteratedFderiv, ← ContinuousMultilinearMap.map_smul_univ]; simp
 #align iterated_fderiv_apply_eq_iterated_deriv_mul_prod iteratedFderiv_apply_eq_iteratedDeriv_mul_prod
 
 theorem norm_iteratedFderiv_eq_norm_iteratedDeriv :
@@ -275,18 +261,11 @@ theorem norm_iteratedFderiv_eq_norm_iteratedDeriv :
 #align norm_iterated_fderiv_eq_norm_iterated_deriv norm_iteratedFderiv_eq_norm_iteratedDeriv
 
 @[simp]
-theorem iteratedDeriv_zero : iteratedDeriv 0 f = f :=
-  by
-  ext x
-  simp [iteratedDeriv]
+theorem iteratedDeriv_zero : iteratedDeriv 0 f = f := by ext x; simp [iteratedDeriv]
 #align iterated_deriv_zero iteratedDeriv_zero
 
 @[simp]
-theorem iteratedDeriv_one : iteratedDeriv 1 f = deriv f :=
-  by
-  ext x
-  simp [iteratedDeriv]
-  rfl
+theorem iteratedDeriv_one : iteratedDeriv 1 f = deriv f := by ext x; simp [iteratedDeriv]; rfl
 #align iterated_deriv_one iteratedDeriv_one
 
 /-- The property of being `C^n`, initially defined in terms of the Fréchet derivative, can be
@@ -341,9 +320,7 @@ theorem iteratedDeriv_eq_iterate : iteratedDeriv n f = (deriv^[n]) f :=
 
 /-- The `n+1`-th iterated derivative can be obtained by taking the `n`-th derivative of the
 derivative. -/
-theorem iteratedDeriv_succ' : iteratedDeriv (n + 1) f = iteratedDeriv n (deriv f) :=
-  by
-  rw [iteratedDeriv_eq_iterate, iteratedDeriv_eq_iterate]
-  rfl
+theorem iteratedDeriv_succ' : iteratedDeriv (n + 1) f = iteratedDeriv n (deriv f) := by
+  rw [iteratedDeriv_eq_iterate, iteratedDeriv_eq_iterate]; rfl
 #align iterated_deriv_succ' iteratedDeriv_succ'
 

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

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! leanprover-community/mathlib commit 3a69562db5a458db8322b190ec8d9a8bbd8a5b14
+! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.Calculus.Deriv
+import Mathbin.Analysis.Calculus.Deriv.Comp
 import Mathbin.Analysis.Calculus.ContDiffDef
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit 3a69562db5a458db8322b190ec8d9a8bbd8a5b14
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -129,10 +129,10 @@ theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f :=
 #align iterated_deriv_within_zero iteratedDerivWithin_zero
 
 @[simp]
-theorem iteratedDerivWithin_one (hs : UniqueDiffOn 𝕜 s) {x : 𝕜} (hx : x ∈ s) :
+theorem iteratedDerivWithin_one {x : 𝕜} (h : UniqueDiffWithinAt 𝕜 s x) :
     iteratedDerivWithin 1 f s x = derivWithin f s x :=
   by
-  simp [iteratedDerivWithin, iteratedFderivWithin_one_apply hs hx]
+  simp only [iteratedDerivWithin, iteratedFderivWithin_one_apply h]
   rfl
 #align iterated_deriv_within_one iteratedDerivWithin_one
 
@@ -170,14 +170,20 @@ theorem ContDiffOn.continuousOn_iteratedDerivWithin {n : ℕ∞} {m : ℕ} (h :
     h.continuous_on_iterated_fderiv_within hmn hs
 #align cont_diff_on.continuous_on_iterated_deriv_within ContDiffOn.continuousOn_iteratedDerivWithin
 
+theorem ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin {n : ℕ∞} {m : ℕ}
+    (h : ContDiffWithinAt 𝕜 n f s x) (hmn : (m : ℕ∞) < n) (hs : UniqueDiffOn 𝕜 (insert x s)) :
+    DifferentiableWithinAt 𝕜 (iteratedDerivWithin m f s) s x := by
+  simpa only [iteratedDerivWithin_eq_equiv_comp,
+    LinearIsometryEquiv.comp_differentiableWithinAt_iff] using
+    h.differentiable_within_at_iterated_fderiv_within hmn hs
+#align cont_diff_within_at.differentiable_within_at_iterated_deriv_within ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin
+
 /-- On a set with unique derivatives, a `C^n` function has derivatives less than `n` which are
 differentiable. -/
 theorem ContDiffOn.differentiableOn_iteratedDerivWithin {n : ℕ∞} {m : ℕ} (h : ContDiffOn 𝕜 n f s)
     (hmn : (m : ℕ∞) < n) (hs : UniqueDiffOn 𝕜 s) :
-    DifferentiableOn 𝕜 (iteratedDerivWithin m f s) s := by
-  simpa only [iteratedDerivWithin_eq_equiv_comp,
-    LinearIsometryEquiv.comp_differentiableOn_iff] using
-    h.differentiable_on_iterated_fderiv_within hmn hs
+    DifferentiableOn 𝕜 (iteratedDerivWithin m f s) s := fun x hx =>
+  (h x hx).differentiableWithinAt_iteratedDerivWithin hmn <| by rwa [insert_eq_of_mem hx]
 #align cont_diff_on.differentiable_on_iterated_deriv_within ContDiffOn.differentiableOn_iteratedDerivWithin
 
 /-- The property of being `C^n`, initially defined in terms of the Fréchet derivative, can be
@@ -215,7 +221,7 @@ theorem iteratedDerivWithin_eq_iterate {x : 𝕜} (hs : UniqueDiffOn 𝕜 s) (hx
   induction' n with n IH generalizing x
   · simp
   · rw [iteratedDerivWithin_succ (hs x hx), Function.iterate_succ']
-    exact derivWithin_congr (hs x hx) (fun y hy => IH hy) (IH hx)
+    exact derivWithin_congr (fun y hy => IH hy) (IH hx)
 #align iterated_deriv_within_eq_iterate iteratedDerivWithin_eq_iterate
 
 /-- The `n+1`-th iterated derivative within a set with unique derivatives can be obtained by

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! leanprover-community/mathlib commit d524d0a578db1146460c1aca35bb5db68466347a
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Deriv
-import Mathbin.Analysis.Calculus.ContDiff
+import Mathbin.Analysis.Calculus.ContDiffDef
 
 /-!
 # One-dimensional iterated derivatives

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit d524d0a578db1146460c1aca35bb5db68466347a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -116,6 +116,11 @@ theorem iteratedFderivWithin_apply_eq_iteratedDerivWithin_mul_prod {m : Fin n 
   simp
 #align iterated_fderiv_within_apply_eq_iterated_deriv_within_mul_prod iteratedFderivWithin_apply_eq_iteratedDerivWithin_mul_prod
 
+theorem norm_iteratedFderivWithin_eq_norm_iteratedDerivWithin :
+    ‖iteratedFderivWithin 𝕜 n f s x‖ = ‖iteratedDerivWithin n f s x‖ := by
+  rw [iteratedDerivWithin_eq_equiv_comp, LinearIsometryEquiv.norm_map]
+#align norm_iterated_fderiv_within_eq_norm_iterated_deriv_within norm_iteratedFderivWithin_eq_norm_iteratedDerivWithin
+
 @[simp]
 theorem iteratedDerivWithin_zero : iteratedDerivWithin 0 f s = f :=
   by
@@ -258,6 +263,11 @@ theorem iteratedFderiv_apply_eq_iteratedDeriv_mul_prod {m : Fin n → 𝕜} :
   simp
 #align iterated_fderiv_apply_eq_iterated_deriv_mul_prod iteratedFderiv_apply_eq_iteratedDeriv_mul_prod
 
+theorem norm_iteratedFderiv_eq_norm_iteratedDeriv :
+    ‖iteratedFderiv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖ := by
+  rw [iteratedDeriv_eq_equiv_comp, LinearIsometryEquiv.norm_map]
+#align norm_iterated_fderiv_eq_norm_iterated_deriv norm_iteratedFderiv_eq_norm_iteratedDeriv
+
 @[simp]
 theorem iteratedDeriv_zero : iteratedDeriv 0 f = f :=
   by

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

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)

@@ -50,9 +50,7 @@ open scoped Classical Topology BigOperators
 open Filter Asymptotics Set
 
 variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
-
 variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-
 variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
 /-- The `n`-th iterated derivative of a function from `𝕜` to `F`, as a function from `𝕜` to `F`. -/

This matches the generality of the non-continuous versions.

The norm_smulRight lemma is the only new result.

@@ -187,7 +187,7 @@ theorem iteratedDerivWithin_succ {x : 𝕜} (hxs : UniqueDiffWithinAt 𝕜 s x)
     iteratedDerivWithin (n + 1) f s x = derivWithin (iteratedDerivWithin n f s) s x := by
   rw [iteratedDerivWithin_eq_iteratedFDerivWithin, iteratedFDerivWithin_succ_apply_left,
     iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_fderivWithin _ hxs, derivWithin]
-  change ((ContinuousMultilinearMap.mkPiField 𝕜 (Fin n) ((fderivWithin 𝕜
+  change ((ContinuousMultilinearMap.mkPiRing 𝕜 (Fin n) ((fderivWithin 𝕜
     (iteratedDerivWithin n f s) s x : 𝕜 → F) 1) : (Fin n → 𝕜) → F) fun i : Fin n => 1) =
     (fderivWithin 𝕜 (iteratedDerivWithin n f s) s x : 𝕜 → F) 1
   simp

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

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathlib.Analysis.Calculus.Deriv.Comp
+import Mathlib.Analysis.Calculus.Deriv.Basic
 import Mathlib.Analysis.Calculus.ContDiff.Defs
 
 #align_import analysis.calculus.iterated_deriv from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"

• Merge Function.left_id and Function.comp.left_id into Function.id_comp.
• Merge Function.right_id and Function.comp.right_id into Function.comp_id.
• Merge Function.comp_const_right and Function.comp_const into Function.comp_const, use explicit arguments.
• Move Function.const_comp to Mathlib.Init.Function, use explicit arguments.

@@ -94,7 +94,7 @@ theorem iteratedFDerivWithin_eq_equiv_comp :
     iteratedFDerivWithin 𝕜 n f s =
       ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDerivWithin n f s := by
   rw [iteratedDerivWithin_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
-    Function.left_id]
+    Function.id_comp]
 #align iterated_fderiv_within_eq_equiv_comp iteratedFDerivWithin_eq_equiv_comp
 
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative
@@ -230,7 +230,7 @@ iterated derivative. -/
 theorem iteratedFDeriv_eq_equiv_comp : iteratedFDeriv 𝕜 n f =
     ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F ∘ iteratedDeriv n f := by
   rw [iteratedDeriv_eq_equiv_comp, ← Function.comp.assoc, LinearIsometryEquiv.self_comp_symm,
-    Function.left_id]
+    Function.id_comp]
 #align iterated_fderiv_eq_equiv_comp iteratedFDeriv_eq_equiv_comp
 
 /-- The `n`-th Fréchet derivative applied to a vector `(m 0, ..., m (n-1))` is the derivative

No changes to content, or splitting, just a rename so there is room for more files.

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Mathlib.Analysis.Calculus.Deriv.Comp
-import Mathlib.Analysis.Calculus.ContDiffDef
+import Mathlib.Analysis.Calculus.ContDiff.Defs
 
 #align_import analysis.calculus.iterated_deriv from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
 

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

This has nice performance benefits.

@@ -49,11 +49,11 @@ open scoped Classical Topology BigOperators
 
 open Filter Asymptotics Set
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜]
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
 
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
 /-- The `n`-th iterated derivative of a function from `𝕜` to `F`, as a function from `𝕜` to `F`. -/
 def iteratedDeriv (n : ℕ) (f : 𝕜 → F) (x : 𝕜) : F :=

• 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) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.calculus.iterated_deriv
-! 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.ContDiffDef
 
+#align_import analysis.calculus.iterated_deriv from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-!
 # One-dimensional iterated derivatives
 

@@ -199,7 +199,7 @@ theorem iteratedDerivWithin_succ {x : 𝕜} (hxs : UniqueDiffWithinAt 𝕜 s x)
 /-- The `n`-th iterated derivative within a set with unique derivatives can be obtained by
 iterating `n` times the differentiation operation. -/
 theorem iteratedDerivWithin_eq_iterate {x : 𝕜} (hs : UniqueDiffOn 𝕜 s) (hx : x ∈ s) :
-    iteratedDerivWithin n f s x = ((fun g : 𝕜 → F => derivWithin g s)^[n]) f x := by
+    iteratedDerivWithin n f s x = (fun g : 𝕜 → F => derivWithin g s)^[n] f x := by
   induction' n with n IH generalizing x
   · simp
   · rw [iteratedDerivWithin_succ (hs x hx), Function.iterate_succ']
@@ -295,7 +295,7 @@ theorem iteratedDeriv_succ : iteratedDeriv (n + 1) f = deriv (iteratedDeriv n f)
 
 /-- The `n`-th iterated derivative can be obtained by iterating `n` times the
 differentiation operation. -/
-theorem iteratedDeriv_eq_iterate : iteratedDeriv n f = (deriv^[n]) f := by
+theorem iteratedDeriv_eq_iterate : iteratedDeriv n f = deriv^[n] f := by
   ext x
   rw [← iteratedDerivWithin_univ]
   convert iteratedDerivWithin_eq_iterate uniqueDiffOn_univ (F := F) (mem_univ x)