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chore: avoid importing ContDiff.Defs in FDeriv.Analytic (#19374)
For this, move the results needing `ContDiff` to two new files. The reason of this change is that I will import `FDeriv.Analytic` in `ContDiff.Defs` in #17152
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Mathlib.lean

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@@ -1120,8 +1120,10 @@ import Mathlib.Analysis.Calculus.BumpFunction.InnerProduct
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import Mathlib.Analysis.Calculus.BumpFunction.Normed
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import Mathlib.Analysis.Calculus.Conformal.InnerProduct
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import Mathlib.Analysis.Calculus.Conformal.NormedSpace
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import Mathlib.Analysis.Calculus.ContDiff.Analytic
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import Mathlib.Analysis.Calculus.ContDiff.Basic
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import Mathlib.Analysis.Calculus.ContDiff.Bounds
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import Mathlib.Analysis.Calculus.ContDiff.CPolynomial
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import Mathlib.Analysis.Calculus.ContDiff.Defs
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import Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries
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import Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno

Mathlib/Analysis/Analytic/Within.lean

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@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Geoffrey Irving
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-/
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import Mathlib.Analysis.Analytic.Constructions
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import Mathlib.Analysis.Analytic.ChangeOrigin
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/-!
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# Properties of analyticity restricted to a set
@@ -40,8 +41,8 @@ lemma analyticWithinAt_of_singleton_mem {f : E → F} {s : Set E} {x : E} (h : {
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AnalyticWithinAt 𝕜 f s x := by
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rcases mem_nhdsWithin.mp h with ⟨t, ot, xt, st⟩
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rcases Metric.mem_nhds_iff.mp (ot.mem_nhds xt) with ⟨r, r0, rt⟩
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exact ⟨constFormalMultilinearSeries 𝕜 E (f x), .ofReal r, {
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r_le := by simp only [FormalMultilinearSeries.constFormalMultilinearSeries_radius, le_top]
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exact ⟨constFormalMultilinearSeries 𝕜 E (f x), .ofReal r,
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{ r_le := by simp only [FormalMultilinearSeries.constFormalMultilinearSeries_radius, le_top]
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r_pos := by positivity
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hasSum := by
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intro y ys yr
@@ -63,10 +64,10 @@ lemma analyticOn_of_locally_analyticOn {f : E → F} {s : Set E}
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rcases h x m with ⟨u, ou, xu, fu⟩
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rcases Metric.mem_nhds_iff.mp (ou.mem_nhds xu) with ⟨r, r0, ru⟩
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rcases fu x ⟨m, xu⟩ with ⟨p, t, fp⟩
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exact ⟨p, min (.ofReal r) t, {
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r_pos := lt_min (by positivity) fp.r_pos
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r_le := min_le_of_right_le fp.r_le
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hasSum := by
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exact ⟨p, min (.ofReal r) t,
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{ r_pos := lt_min (by positivity) fp.r_pos
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r_le := min_le_of_right_le fp.r_le
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hasSum := by
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intro y ys yr
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simp only [EMetric.mem_ball, lt_min_iff, edist_lt_ofReal, dist_zero_right] at yr
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apply fp.hasSum
@@ -88,8 +89,8 @@ lemma IsOpen.analyticOn_iff_analyticOnNhd {f : E → F} {s : Set E} (hs : IsOpen
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intro hf x m
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rcases Metric.mem_nhds_iff.mp (hs.mem_nhds m) with ⟨r, r0, rs⟩
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rcases hf x m with ⟨p, t, fp⟩
91-
exact ⟨p, min (.ofReal r) t, {
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r_pos := lt_min (by positivity) fp.r_pos
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exact ⟨p, min (.ofReal r) t,
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{ r_pos := lt_min (by positivity) fp.r_pos
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r_le := min_le_of_right_le fp.r_le
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hasSum := by
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intro y ym
@@ -200,3 +201,15 @@ lemma analyticWithinAt_iff_exists_analyticAt' [CompleteSpace F] {f : E → F} {s
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exact ⟨g, by filter_upwards [self_mem_nhdsWithin] using hf, hg⟩
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alias ⟨AnalyticWithinAt.exists_analyticAt, _⟩ := analyticWithinAt_iff_exists_analyticAt'
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lemma AnalyticWithinAt.exists_mem_nhdsWithin_analyticOn
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[CompleteSpace F] {f : E → F} {s : Set E} {x : E} (h : AnalyticWithinAt 𝕜 f s x) :
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∃ u ∈ 𝓝[insert x s] x, AnalyticOn 𝕜 f u := by
208+
obtain ⟨g, -, h'g, hg⟩ : ∃ g, f x = g x ∧ EqOn f g (insert x s) ∧ AnalyticAt 𝕜 g x :=
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h.exists_analyticAt
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let u := insert x s ∩ {y | AnalyticAt 𝕜 g y}
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refine ⟨u, ?_, ?_⟩
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· exact inter_mem_nhdsWithin _ ((isOpen_analyticAt 𝕜 g).mem_nhds hg)
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· intro y hy
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have : AnalyticWithinAt 𝕜 g u y := hy.2.analyticWithinAt
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exact this.congr (h'g.mono (inter_subset_left)) (h'g (inter_subset_left hy))
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/-
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Copyright (c) 2021 Yury Kudryashov. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Yury Kudryashov
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-/
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import Mathlib.Analysis.Calculus.ContDiff.Defs
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import Mathlib.Analysis.Calculus.FDeriv.Analytic
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/-!
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# Analytic functions are `C^∞`.
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-/
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open Set ContDiff
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variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
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{E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
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{F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
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{f : E → F} {s : Set E} {x : E} {n : WithTop ℕ∞}
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/-- An analytic function is infinitely differentiable. -/
21+
protected theorem AnalyticOnNhd.contDiffOn [CompleteSpace F] (h : AnalyticOnNhd 𝕜 f s) :
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ContDiffOn 𝕜 n f s := by
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let t := { x | AnalyticAt 𝕜 f x }
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suffices ContDiffOn 𝕜 ω f t from (this.of_le le_top).mono h
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rw [← contDiffOn_infty_iff_contDiffOn_omega]
26+
have H : AnalyticOnNhd 𝕜 f t := fun _x hx ↦ hx
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have t_open : IsOpen t := isOpen_analyticAt 𝕜 f
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exact contDiffOn_of_continuousOn_differentiableOn
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(fun m _ ↦ (H.iteratedFDeriv m).continuousOn.congr
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fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
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(fun m _ ↦ (H.iteratedFDeriv m).differentiableOn.congr
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fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
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/-- An analytic function on the whole space is infinitely differentiable there. -/
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theorem AnalyticOnNhd.contDiff [CompleteSpace F] (h : AnalyticOnNhd 𝕜 f univ) :
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ContDiff 𝕜 n f := by
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rw [← contDiffOn_univ]
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exact h.contDiffOn
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theorem AnalyticAt.contDiffAt [CompleteSpace F] (h : AnalyticAt 𝕜 f x) {n : ℕ∞} :
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ContDiffAt 𝕜 n f x := by
42+
obtain ⟨s, hs, hf⟩ := h.exists_mem_nhds_analyticOnNhd
43+
exact hf.contDiffOn.contDiffAt hs
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protected lemma AnalyticWithinAt.contDiffWithinAt [CompleteSpace F] {f : E → F} {s : Set E} {x : E}
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(h : AnalyticWithinAt 𝕜 f s x) {n : ℕ∞} : ContDiffWithinAt 𝕜 n f s x := by
47+
rcases h.exists_analyticAt with ⟨g, fx, fg, hg⟩
48+
exact hg.contDiffAt.contDiffWithinAt.congr (fg.mono (subset_insert _ _)) fx
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protected lemma AnalyticOn.contDiffOn [CompleteSpace F] {f : E → F} {s : Set E}
51+
(h : AnalyticOn 𝕜 f s) {n : ℕ∞} : ContDiffOn 𝕜 n f s :=
52+
fun x m ↦ (h x m).contDiffWithinAt
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54+
@[deprecated (since := "2024-09-26")]
55+
alias AnalyticWithinOn.contDiffOn := AnalyticOn.contDiffOn
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@@ -0,0 +1,63 @@
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/-
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Copyright (c) 2021 Yury Kudryashov. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Yury Kudryashov
5+
-/
6+
import Mathlib.Analysis.Calculus.FDeriv.Analytic
7+
import Mathlib.Analysis.Calculus.ContDiff.Defs
8+
9+
/-!
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# Higher smoothness of continuously polynomial functions
11+
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We prove that continuously polynomial functions are `C^∞`. In particular, this is the case
13+
of continuous multilinear maps.
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-/
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open Filter Asymptotics
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open scoped ENNReal ContDiff
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universe u v
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variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
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variable {E : Type u} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
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variable {F : Type v} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
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section fderiv
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variable {p : FormalMultilinearSeries 𝕜 E F} {r : ℝ≥0∞} {n : ℕ}
29+
variable {f : E → F} {x : E} {s : Set E}
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31+
/-- A polynomial function is infinitely differentiable. -/
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theorem CPolynomialOn.contDiffOn (h : CPolynomialOn 𝕜 f s) {n : WithTop ℕ∞} :
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ContDiffOn 𝕜 n f s := by
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let t := { x | CPolynomialAt 𝕜 f x }
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suffices ContDiffOn 𝕜 ω f t from (this.of_le le_top).mono h
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rw [← contDiffOn_infty_iff_contDiffOn_omega]
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have H : CPolynomialOn 𝕜 f t := fun _x hx ↦ hx
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have t_open : IsOpen t := isOpen_cPolynomialAt 𝕜 f
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exact contDiffOn_of_continuousOn_differentiableOn
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(fun m _ ↦ (H.iteratedFDeriv m).continuousOn.congr
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fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
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(fun m _ ↦ (H.iteratedFDeriv m).analyticOnNhd.differentiableOn.congr
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fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
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45+
theorem CPolynomialAt.contDiffAt (h : CPolynomialAt 𝕜 f x) {n : WithTop ℕ∞} :
46+
ContDiffAt 𝕜 n f x :=
47+
let ⟨_, hs, hf⟩ := h.exists_mem_nhds_cPolynomialOn
48+
hf.contDiffOn.contDiffAt hs
49+
50+
end fderiv
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52+
namespace ContinuousMultilinearMap
53+
54+
variable {ι : Type*} {E : ι → Type*} [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)]
55+
[Fintype ι] (f : ContinuousMultilinearMap 𝕜 E F) {n : WithTop ℕ∞} {x : Π i, E i}
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57+
open FormalMultilinearSeries
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59+
lemma contDiffAt : ContDiffAt 𝕜 n f x := f.cpolynomialAt.contDiffAt
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61+
lemma contDiff : ContDiff 𝕜 n f := contDiff_iff_contDiffAt.mpr (fun _ ↦ f.contDiffAt)
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63+
end ContinuousMultilinearMap

Mathlib/Analysis/Calculus/FDeriv/Analytic.lean

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@@ -7,7 +7,7 @@ import Mathlib.Analysis.Analytic.CPolynomial
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import Mathlib.Analysis.Analytic.Inverse
88
import Mathlib.Analysis.Analytic.Within
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import Mathlib.Analysis.Calculus.Deriv.Basic
10-
import Mathlib.Analysis.Calculus.ContDiff.Defs
10+
import Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries
1111
import Mathlib.Analysis.Calculus.FDeriv.Add
1212
import Mathlib.Analysis.Calculus.FDeriv.Prod
1313
import Mathlib.Analysis.Normed.Module.Completion
@@ -63,7 +63,7 @@ differentiability at points in a neighborhood of `s`. Therefore, the theorem tha
6363

6464
open Filter Asymptotics Set
6565

66-
open scoped ENNReal Topology ContDiff
66+
open scoped ENNReal Topology
6767

6868
universe u v
6969

@@ -192,6 +192,7 @@ theorem HasFPowerSeriesOnBall.fderiv_eq [CompleteSpace F] (h : HasFPowerSeriesOn
192192
fderiv 𝕜 f (x + y) = continuousMultilinearCurryFin1 𝕜 E F (p.changeOrigin y 1) :=
193193
(h.hasFDerivAt hy).fderiv
194194

195+
/-- If a function has a power series on a ball, then so does its derivative. -/
195196
protected theorem HasFPowerSeriesOnBall.fderiv [CompleteSpace F]
196197
(h : HasFPowerSeriesOnBall f p x r) :
197198
HasFPowerSeriesOnBall (fderiv 𝕜 f) p.derivSeries x r := by
@@ -238,7 +239,7 @@ protected theorem AnalyticOnNhd.fderiv [CompleteSpace F] (h : AnalyticOnNhd 𝕜
238239
alias AnalyticOn.fderiv := AnalyticOnNhd.fderiv
239240

240241
/-- If a function is analytic on a set `s`, so are its successive Fréchet derivative. See also
241-
`AnalyticOnNhd.iteratedFDeruv_of_isOpen`, removing the completeness assumption but requiring the set
242+
`AnalyticOnNhd.iteratedFDeriv_of_isOpen`, removing the completeness assumption but requiring the set
242243
to be open.-/
243244
protected theorem AnalyticOnNhd.iteratedFDeriv [CompleteSpace F] (h : AnalyticOnNhd 𝕜 f s) (n : ℕ) :
244245
AnalyticOnNhd 𝕜 (iteratedFDeriv 𝕜 n f) s := by
@@ -269,44 +270,6 @@ lemma AnalyticOnNhd.hasFTaylorSeriesUpToOn [CompleteSpace F]
269270
· apply (DifferentiableAt.continuousAt (𝕜 := 𝕜) ?_).continuousWithinAt
270271
exact (h.iteratedFDeriv m x hx).differentiableAt
271272

272-
/-- An analytic function is infinitely differentiable. -/
273-
protected theorem AnalyticOnNhd.contDiffOn [CompleteSpace F] (h : AnalyticOnNhd 𝕜 f s)
274-
{n : WithTop ℕ∞} : ContDiffOn 𝕜 n f s := by
275-
suffices ContDiffOn 𝕜 ω f s from this.of_le le_top
276-
rw [← contDiffOn_infty_iff_contDiffOn_omega]
277-
let t := { x | AnalyticAt 𝕜 f x }
278-
suffices ContDiffOn 𝕜 ∞ f t from this.mono h
279-
have H : AnalyticOnNhd 𝕜 f t := fun _x hx ↦ hx
280-
have t_open : IsOpen t := isOpen_analyticAt 𝕜 f
281-
exact contDiffOn_of_continuousOn_differentiableOn
282-
(fun m _ ↦ (H.iteratedFDeriv m).continuousOn.congr
283-
fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
284-
(fun m _ ↦ (H.iteratedFDeriv m).differentiableOn.congr
285-
fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
286-
287-
/-- An analytic function on the whole space is infinitely differentiable there. -/
288-
theorem AnalyticOnNhd.contDiff [CompleteSpace F] (h : AnalyticOnNhd 𝕜 f univ) {n : WithTop ℕ∞} :
289-
ContDiff 𝕜 n f := by
290-
rw [← contDiffOn_univ]
291-
exact h.contDiffOn
292-
293-
theorem AnalyticAt.contDiffAt [CompleteSpace F] (h : AnalyticAt 𝕜 f x) {n : WithTop ℕ∞} :
294-
ContDiffAt 𝕜 n f x := by
295-
obtain ⟨s, hs, hf⟩ := h.exists_mem_nhds_analyticOnNhd
296-
exact hf.contDiffOn.contDiffAt hs
297-
298-
protected lemma AnalyticWithinAt.contDiffWithinAt [CompleteSpace F] {f : E → F} {s : Set E} {x : E}
299-
(h : AnalyticWithinAt 𝕜 f s x) {n : ℕ∞} : ContDiffWithinAt 𝕜 n f s x := by
300-
rcases h.exists_analyticAt with ⟨g, fx, fg, hg⟩
301-
exact hg.contDiffAt.contDiffWithinAt.congr (fg.mono (subset_insert _ _)) fx
302-
303-
protected lemma AnalyticOn.contDiffOn [CompleteSpace F] {f : E → F} {s : Set E}
304-
(h : AnalyticOn 𝕜 f s) {n : ℕ∞} : ContDiffOn 𝕜 n f s :=
305-
fun x m ↦ (h x m).contDiffWithinAt
306-
307-
@[deprecated (since := "2024-09-26")]
308-
alias AnalyticWithinOn.contDiffOn := AnalyticOn.contDiffOn
309-
310273
lemma AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn [CompleteSpace F]
311274
(n : WithTop ℕ∞) (h : AnalyticWithinAt 𝕜 f s x) :
312275
∃ u ∈ 𝓝[insert x s] x, ∃ (p : E → FormalMultilinearSeries 𝕜 E F),
@@ -384,7 +347,7 @@ protected theorem AnalyticOn.iteratedFDerivWithin (h : AnalyticOn 𝕜 f s)
384347
apply AnalyticOnNhd.comp_analyticOn _ (IH.fderivWithin hu) (mapsTo_univ _ _)
385348
apply LinearIsometryEquiv.analyticOnNhd
386349

387-
lemma AnalyticOn.hasFTaylorSeriesUpToOn {n : WithTop ℕ∞}
350+
protected lemma AnalyticOn.hasFTaylorSeriesUpToOn {n : WithTop ℕ∞}
388351
(h : AnalyticOn 𝕜 f s) (hu : UniqueDiffOn 𝕜 s) :
389352
HasFTaylorSeriesUpToOn n f (ftaylorSeriesWithin 𝕜 f s) s := by
390353
refine ⟨fun x _hx ↦ rfl, fun m _hm x hx ↦ ?_, fun m _hm x hx ↦ ?_⟩
@@ -546,26 +509,6 @@ theorem CPolynomialOn.iteratedFDeriv (h : CPolynomialOn 𝕜 f s) (n : ℕ) :
546509
case g => exact ↑(continuousMultilinearCurryLeftEquiv 𝕜 (fun _ : Fin (n + 1) ↦ E) F).symm
547510
simp
548511

549-
/-- A polynomial function is infinitely differentiable. -/
550-
theorem CPolynomialOn.contDiffOn (h : CPolynomialOn 𝕜 f s) {n : WithTop ℕ∞} :
551-
ContDiffOn 𝕜 n f s := by
552-
suffices ContDiffOn 𝕜 ω f s from this.of_le le_top
553-
let t := { x | CPolynomialAt 𝕜 f x }
554-
suffices ContDiffOn 𝕜 ω f t from this.mono h
555-
rw [← contDiffOn_infty_iff_contDiffOn_omega]
556-
have H : CPolynomialOn 𝕜 f t := fun _x hx ↦ hx
557-
have t_open : IsOpen t := isOpen_cPolynomialAt 𝕜 f
558-
exact contDiffOn_of_continuousOn_differentiableOn
559-
(fun m _ ↦ (H.iteratedFDeriv m).continuousOn.congr
560-
fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
561-
(fun m _ ↦ (H.iteratedFDeriv m).analyticOnNhd.differentiableOn.congr
562-
fun _ hx ↦ iteratedFDerivWithin_of_isOpen _ t_open hx)
563-
564-
theorem CPolynomialAt.contDiffAt (h : CPolynomialAt 𝕜 f x) {n : WithTop ℕ∞} :
565-
ContDiffAt 𝕜 n f x :=
566-
let ⟨_, hs, hf⟩ := h.exists_mem_nhds_cPolynomialOn
567-
hf.contDiffOn.contDiffAt hs
568-
569512
end fderiv
570513

571514
section deriv
@@ -750,10 +693,6 @@ lemma cPolynomialAt : CPolynomialAt 𝕜 f x :=
750693

751694
lemma cPolyomialOn : CPolynomialOn 𝕜 f ⊤ := fun x _ ↦ f.cPolynomialAt x
752695

753-
lemma contDiffAt : ContDiffAt 𝕜 n f x := (f.cPolynomialAt x).contDiffAt
754-
755-
lemma contDiff : ContDiff 𝕜 n f := contDiff_iff_contDiffAt.mpr f.contDiffAt
756-
757696
end ContinuousMultilinearMap
758697

759698
namespace FormalMultilinearSeries
@@ -797,8 +736,8 @@ private theorem factorial_smul' {n : ℕ} : ∀ {F : Type max u v} [NormedAddCom
797736
n ! • p n (fun _ ↦ y) = iteratedFDeriv 𝕜 n f x (fun _ ↦ y) := by
798737
induction n with | zero => _ | succ n ih => _ <;> intro F _ _ _ p f h
799738
· rw [factorial_zero, one_smul, h.iteratedFDeriv_zero_apply_diag]
800-
· rw [factorial_succ, mul_comm, mul_smul, ← derivSeries_apply_diag, ← smul_apply,
801-
ih h.fderiv, iteratedFDeriv_succ_apply_right]
739+
· rw [factorial_succ, mul_comm, mul_smul, ← derivSeries_apply_diag,
740+
← ContinuousLinearMap.smul_apply, ih h.fderiv, iteratedFDeriv_succ_apply_right]
802741
rfl
803742

804743
variable [CompleteSpace F]
@@ -808,8 +747,8 @@ theorem factorial_smul (n : ℕ) :
808747
n ! • p n (fun _ ↦ y) = iteratedFDeriv 𝕜 n f x (fun _ ↦ y) := by
809748
cases n
810749
· rw [factorial_zero, one_smul, h.iteratedFDeriv_zero_apply_diag]
811-
· rw [factorial_succ, mul_comm, mul_smul, ← derivSeries_apply_diag, ← smul_apply,
812-
factorial_smul' _ h.fderiv, iteratedFDeriv_succ_apply_right]
750+
· rw [factorial_succ, mul_comm, mul_smul, ← derivSeries_apply_diag,
751+
← ContinuousLinearMap.smul_apply, factorial_smul' _ h.fderiv, iteratedFDeriv_succ_apply_right]
813752
rfl
814753

815754
theorem hasSum_iteratedFDeriv [CharZero 𝕜] {y : E} (hy : y ∈ EMetric.ball 0 r) :

Mathlib/Analysis/Fourier/FourierTransformDeriv.lean

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
44
Authors: Alex Kontorovich, David Loeffler, Heather Macbeth, Sébastien Gouëzel
55
-/
66
import Mathlib.Analysis.Calculus.ParametricIntegral
7+
import Mathlib.Analysis.Calculus.ContDiff.CPolynomial
78
import Mathlib.Analysis.Fourier.AddCircle
89
import Mathlib.Analysis.Fourier.FourierTransform
910
import Mathlib.Analysis.Calculus.FDeriv.Analytic
@@ -369,7 +370,7 @@ lemma norm_iteratedFDeriv_fourierPowSMulRight
369370
have I₂ m : ‖iteratedFDeriv ℝ m (T ∘ (ContinuousLinearMap.pi (fun (_ : Fin n) ↦ L))) v‖ ≤
370371
(n.descFactorial m * 1 * (‖L‖ * ‖v‖) ^ (n - m)) * ‖L‖ ^ m := by
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rw [ContinuousLinearMap.iteratedFDeriv_comp_right _ (ContinuousMultilinearMap.contDiff _)
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_ le_top]
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_ (mod_cast le_top)]
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apply (norm_compContinuousLinearMap_le _ _).trans
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simp only [Finset.prod_const, Finset.card_fin]
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gcongr

Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean

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@@ -4,7 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
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-/
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import Mathlib.Analysis.Complex.RealDeriv
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import Mathlib.Analysis.Calculus.ContDiff.Analytic
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import Mathlib.Analysis.Calculus.ContDiff.RCLike
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import Mathlib.Analysis.Calculus.FDeriv.Analytic
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import Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas
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import Mathlib.Analysis.SpecialFunctions.Exponential
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Mathlib/Geometry/Manifold/AnalyticManifold.lean

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@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Michael Lee, Geoffrey Irving
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-/
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import Mathlib.Analysis.Analytic.Constructions
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import Mathlib.Analysis.Calculus.FDeriv.Analytic
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import Mathlib.Analysis.Calculus.ContDiff.Analytic
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import Mathlib.Geometry.Manifold.SmoothManifoldWithCorners
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/-!

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