geometry.manifold.whitney_embedding ⟷ Mathlib.Geometry.Manifold.WhitneyEmbedding

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

@@ -78,10 +78,10 @@ theorem embeddingPiTangent_coe :
 theorem embeddingPiTangent_injOn : InjOn f.embeddingPiTangent s :=
   by
   intro x hx y hy h
-  simp only [embedding_pi_tangent_coe, funext_iff] at h 
+  simp only [embedding_pi_tangent_coe, funext_iff] at h
   obtain ⟨h₁, h₂⟩ := Prod.mk.inj_iff.1 (h (f.ind x hx))
-  rw [f.apply_ind x hx] at h₂ 
-  rw [← h₂, f.apply_ind x hx, one_smul, one_smul] at h₁ 
+  rw [f.apply_ind x hx] at h₂
+  rw [← h₂, f.apply_ind x hx, one_smul, one_smul] at h₁
   have := f.mem_ext_chart_at_source_of_eq_one h₂.symm
   exact (extChartAt I (f.c _)).InjOn (f.mem_ext_chart_at_ind_source x hx) this h₁
 #align smooth_bump_covering.embedding_pi_tangent_inj_on SmoothBumpCovering.embeddingPiTangent_injOn

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Geometry.Manifold.Diffeomorph
-import Mathbin.Geometry.Manifold.Instances.Real
-import Mathbin.Geometry.Manifold.PartitionOfUnity
+import Geometry.Manifold.Diffeomorph
+import Geometry.Manifold.Instances.Real
+import Geometry.Manifold.PartitionOfUnity
 
 #align_import geometry.manifold.whitney_embedding from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module geometry.manifold.whitney_embedding
-! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Manifold.Diffeomorph
 import Mathbin.Geometry.Manifold.Instances.Real
 import Mathbin.Geometry.Manifold.PartitionOfUnity
 
+#align_import geometry.manifold.whitney_embedding from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"
+
 /-!
 # Whitney embedding theorem
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a51edf13debfcbe223fa06b1cb353b9ed9751cc

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module geometry.manifold.whitney_embedding
-! leanprover-community/mathlib commit 86c29aefdba50b3f33e86e52e3b2f51a0d8f0282
+! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Geometry.Manifold.PartitionOfUnity
 /-!
 # Whitney embedding theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove a version of the Whitney embedding theorem: for any compact real manifold `M`,
 for sufficiently large `n` there exists a smooth embedding `M → ℝ^n`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -55,6 +55,7 @@ In this section we prove a version of the Whitney embedding theorem: for any com
 
 variable [T2Space M] [hi : Fintype ι] {s : Set M} (f : SmoothBumpCovering ι I M s)
 
+#print SmoothBumpCovering.embeddingPiTangent /-
 /-- Smooth embedding of `M` into `(E × ℝ) ^ ι`. -/
 def embeddingPiTangent : C^∞⟮I, M; 𝓘(ℝ, ι → E × ℝ), ι → E × ℝ⟯
     where
@@ -63,13 +64,17 @@ def embeddingPiTangent : C^∞⟮I, M; 𝓘(ℝ, ι → E × ℝ), ι → E × 
     contMDiff_pi_space.2 fun i =>
       ((f i).smooth_smul contMDiffOn_extChartAt).prod_mk_space (f i).Smooth
 #align smooth_bump_covering.embedding_pi_tangent SmoothBumpCovering.embeddingPiTangent
+-/
 
+#print SmoothBumpCovering.embeddingPiTangent_coe /-
 @[local simp]
 theorem embeddingPiTangent_coe :
     ⇑f.embeddingPiTangent = fun x i => (f i x • extChartAt I (f.c i) x, f i x) :=
   rfl
 #align smooth_bump_covering.embedding_pi_tangent_coe SmoothBumpCovering.embeddingPiTangent_coe
+-/
 
+#print SmoothBumpCovering.embeddingPiTangent_injOn /-
 theorem embeddingPiTangent_injOn : InjOn f.embeddingPiTangent s :=
   by
   intro x hx y hy h
@@ -80,12 +85,16 @@ theorem embeddingPiTangent_injOn : InjOn f.embeddingPiTangent s :=
   have := f.mem_ext_chart_at_source_of_eq_one h₂.symm
   exact (extChartAt I (f.c _)).InjOn (f.mem_ext_chart_at_ind_source x hx) this h₁
 #align smooth_bump_covering.embedding_pi_tangent_inj_on SmoothBumpCovering.embeddingPiTangent_injOn
+-/
 
+#print SmoothBumpCovering.embeddingPiTangent_injective /-
 theorem embeddingPiTangent_injective (f : SmoothBumpCovering ι I M) :
     Injective f.embeddingPiTangent :=
   injective_iff_injOn_univ.2 f.embeddingPiTangent_injOn
 #align smooth_bump_covering.embedding_pi_tangent_injective SmoothBumpCovering.embeddingPiTangent_injective
+-/
 
+#print SmoothBumpCovering.comp_embeddingPiTangent_mfderiv /-
 theorem comp_embeddingPiTangent_mfderiv (x : M) (hx : x ∈ s) :
     ((ContinuousLinearMap.fst ℝ E ℝ).comp
             (@ContinuousLinearMap.proj ℝ _ ι (fun _ => E × ℝ) _ _ (fun _ => inferInstance)
@@ -104,7 +113,9 @@ theorem comp_embeddingPiTangent_mfderiv (x : M) (hx : x ∈ s) :
     ContinuousLinearMap.coe_fst', ContinuousLinearMap.proj_apply]
   rw [hy, Pi.one_apply, one_smul]
 #align smooth_bump_covering.comp_embedding_pi_tangent_mfderiv SmoothBumpCovering.comp_embeddingPiTangent_mfderiv
+-/
 
+#print SmoothBumpCovering.embeddingPiTangent_ker_mfderiv /-
 theorem embeddingPiTangent_ker_mfderiv (x : M) (hx : x ∈ s) :
     LinearMap.ker (mfderiv I 𝓘(ℝ, ι → E × ℝ) f.embeddingPiTangent x) = ⊥ :=
   by
@@ -115,12 +126,16 @@ theorem embeddingPiTangent_ker_mfderiv (x : M) (hx : x ∈ s) :
     ← comp_embedding_pi_tangent_mfderiv]
   exact LinearMap.ker_le_ker_comp _ _
 #align smooth_bump_covering.embedding_pi_tangent_ker_mfderiv SmoothBumpCovering.embeddingPiTangent_ker_mfderiv
+-/
 
+#print SmoothBumpCovering.embeddingPiTangent_injective_mfderiv /-
 theorem embeddingPiTangent_injective_mfderiv (x : M) (hx : x ∈ s) :
     Injective (mfderiv I 𝓘(ℝ, ι → E × ℝ) f.embeddingPiTangent x) :=
   LinearMap.ker_eq_bot.1 (f.embeddingPiTangent_ker_mfderiv x hx)
 #align smooth_bump_covering.embedding_pi_tangent_injective_mfderiv SmoothBumpCovering.embeddingPiTangent_injective_mfderiv
+-/
 
+#print SmoothBumpCovering.exists_immersion_euclidean /-
 /-- Baby version of the **Whitney weak embedding theorem**: if `M` admits a finite covering by
 supports of bump functions, then for some `n` it can be immersed into the `n`-dimensional
 Euclidean space. -/
@@ -142,9 +157,11 @@ theorem exists_immersion_euclidean [Finite ι] (f : SmoothBumpCovering ι I M) :
     eEF.mfderiv_eq]
   exact eEF.injective.comp (f.embedding_pi_tangent_injective_mfderiv _ trivial)
 #align smooth_bump_covering.exists_immersion_euclidean SmoothBumpCovering.exists_immersion_euclidean
+-/
 
 end SmoothBumpCovering
 
+#print exists_embedding_euclidean_of_compact /-
 /-- Baby version of the Whitney weak embedding theorem: if `M` admits a finite covering by
 supports of bump functions, then for some `n` it can be embedded into the `n`-dimensional
 Euclidean space. -/
@@ -158,4 +175,5 @@ theorem exists_embedding_euclidean_of_compact [T2Space M] [CompactSpace M] :
   rcases f.exists_immersion_euclidean with ⟨n, e, hsmooth, hinj, hinj_mfderiv⟩
   exact ⟨n, e, hsmooth, hsmooth.continuous.closed_embedding hinj, hinj_mfderiv⟩
 #align exists_embedding_euclidean_of_compact exists_embedding_euclidean_of_compact
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -97,8 +97,8 @@ theorem comp_embeddingPiTangent_mfderiv (x : M) (hx : x ∈ s) :
     (ContinuousLinearMap.fst ℝ E ℝ).comp
       (@ContinuousLinearMap.proj ℝ _ ι (fun _ => E × ℝ) _ _ (fun _ => inferInstance) (f.ind x hx))
   have := L.has_mfderiv_at.comp x f.embedding_pi_tangent.mdifferentiable_at.has_mfderiv_at
-  convert hasMfderivAt_unique this _
-  refine' (hasMfderivAt_extChartAt I (f.mem_chart_at_ind_source x hx)).congr_of_eventuallyEq _
+  convert hasMFDerivAt_unique this _
+  refine' (hasMFDerivAt_extChartAt I (f.mem_chart_at_ind_source x hx)).congr_of_eventuallyEq _
   refine' (f.eventually_eq_one x hx).mono fun y hy => _
   simp only [embedding_pi_tangent_coe, ContinuousLinearMap.coe_comp', (· ∘ ·),
     ContinuousLinearMap.coe_fst', ContinuousLinearMap.proj_apply]

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

@@ -60,8 +60,8 @@ def embeddingPiTangent : C^∞⟮I, M; 𝓘(ℝ, ι → E × ℝ), ι → E × 
     where
   val x i := (f i x • extChartAt I (f.c i) x, f i x)
   property :=
-    contMdiff_pi_space.2 fun i =>
-      ((f i).smooth_smul contMdiffOn_extChartAt).prod_mk_space (f i).Smooth
+    contMDiff_pi_space.2 fun i =>
+      ((f i).smooth_smul contMDiffOn_extChartAt).prod_mk_space (f i).Smooth
 #align smooth_bump_covering.embedding_pi_tangent SmoothBumpCovering.embeddingPiTangent
 
 @[local simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module geometry.manifold.whitney_embedding
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 86c29aefdba50b3f33e86e52e3b2f51a0d8f0282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -58,8 +58,8 @@ variable [T2Space M] [hi : Fintype ι] {s : Set M} (f : SmoothBumpCovering ι I
 /-- Smooth embedding of `M` into `(E × ℝ) ^ ι`. -/
 def embeddingPiTangent : C^∞⟮I, M; 𝓘(ℝ, ι → E × ℝ), ι → E × ℝ⟯
     where
-  toFun x i := (f i x • extChartAt I (f.c i) x, f i x)
-  contMdiff_toFun :=
+  val x i := (f i x • extChartAt I (f.c i) x, f i x)
+  property :=
     contMdiff_pi_space.2 fun i =>
       ((f i).smooth_smul contMdiffOn_extChartAt).prod_mk_space (f i).Smooth
 #align smooth_bump_covering.embedding_pi_tangent SmoothBumpCovering.embeddingPiTangent

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

@@ -55,8 +55,6 @@ In this section we prove a version of the Whitney embedding theorem: for any com
 
 variable [T2Space M] [hi : Fintype ι] {s : Set M} (f : SmoothBumpCovering ι I M s)
 
-include hi
-
 /-- Smooth embedding of `M` into `(E × ℝ) ^ ι`. -/
 def embeddingPiTangent : C^∞⟮I, M; 𝓘(ℝ, ι → E × ℝ), ι → E × ℝ⟯
     where
@@ -123,8 +121,6 @@ theorem embeddingPiTangent_injective_mfderiv (x : M) (hx : x ∈ s) :
   LinearMap.ker_eq_bot.1 (f.embeddingPiTangent_ker_mfderiv x hx)
 #align smooth_bump_covering.embedding_pi_tangent_injective_mfderiv SmoothBumpCovering.embeddingPiTangent_injective_mfderiv
 
-omit hi
-
 /-- Baby version of the **Whitney weak embedding theorem**: if `M` admits a finite covering by
 supports of bump functions, then for some `n` it can be immersed into the `n`-dimensional
 Euclidean space. -/

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

@@ -75,10 +75,10 @@ theorem embeddingPiTangent_coe :
 theorem embeddingPiTangent_injOn : InjOn f.embeddingPiTangent s :=
   by
   intro x hx y hy h
-  simp only [embedding_pi_tangent_coe, funext_iff] at h
+  simp only [embedding_pi_tangent_coe, funext_iff] at h 
   obtain ⟨h₁, h₂⟩ := Prod.mk.inj_iff.1 (h (f.ind x hx))
-  rw [f.apply_ind x hx] at h₂
-  rw [← h₂, f.apply_ind x hx, one_smul, one_smul] at h₁
+  rw [f.apply_ind x hx] at h₂ 
+  rw [← h₂, f.apply_ind x hx, one_smul, one_smul] at h₁ 
   have := f.mem_ext_chart_at_source_of_eq_one h₂.symm
   exact (extChartAt I (f.c _)).InjOn (f.mem_ext_chart_at_ind_source x hx) this h₁
 #align smooth_bump_covering.embedding_pi_tangent_inj_on SmoothBumpCovering.embeddingPiTangent_injOn
@@ -129,7 +129,7 @@ omit hi
 supports of bump functions, then for some `n` it can be immersed into the `n`-dimensional
 Euclidean space. -/
 theorem exists_immersion_euclidean [Finite ι] (f : SmoothBumpCovering ι I M) :
-    ∃ (n : ℕ)(e : M → EuclideanSpace ℝ (Fin n)),
+    ∃ (n : ℕ) (e : M → EuclideanSpace ℝ (Fin n)),
       Smooth I (𝓡 n) e ∧ Injective e ∧ ∀ x : M, Injective (mfderiv I (𝓡 n) e x) :=
   by
   cases nonempty_fintype ι
@@ -153,7 +153,7 @@ end SmoothBumpCovering
 supports of bump functions, then for some `n` it can be embedded into the `n`-dimensional
 Euclidean space. -/
 theorem exists_embedding_euclidean_of_compact [T2Space M] [CompactSpace M] :
-    ∃ (n : ℕ)(e : M → EuclideanSpace ℝ (Fin n)),
+    ∃ (n : ℕ) (e : M → EuclideanSpace ℝ (Fin n)),
       Smooth I (𝓡 n) e ∧ ClosedEmbedding e ∧ ∀ x : M, Injective (mfderiv I (𝓡 n) e x) :=
   by
   rcases SmoothBumpCovering.exists_isSubordinate I isClosed_univ fun (x : M) _ => univ_mem with

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

@@ -39,7 +39,7 @@ variable {ι : Type uι} {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E
 
 open Function Filter FiniteDimensional Set
 
-open Topology Manifold Classical Filter BigOperators
+open scoped Topology Manifold Classical Filter BigOperators
 
 noncomputable section
 

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

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

@@ -93,7 +93,7 @@ theorem comp_embeddingPiTangent_mfderiv (x : M) (hx : x ∈ s) :
   convert hasMFDerivAt_unique this _
   refine' (hasMFDerivAt_extChartAt I (f.mem_chartAt_ind_source x hx)).congr_of_eventuallyEq _
   refine' (f.eventuallyEq_one x hx).mono fun y hy => _
-  simp only [embeddingPiTangent_coe, ContinuousLinearMap.coe_comp', (· ∘ ·),
+  simp only [L, embeddingPiTangent_coe, ContinuousLinearMap.coe_comp', (· ∘ ·),
     ContinuousLinearMap.coe_fst', ContinuousLinearMap.proj_apply]
   rw [hy, Pi.one_apply, one_smul]
 #align smooth_bump_covering.comp_embedding_pi_tangent_mfderiv SmoothBumpCovering.comp_embeddingPiTangent_mfderiv

@@ -67,10 +67,10 @@ theorem embeddingPiTangent_coe :
 
 theorem embeddingPiTangent_injOn : InjOn f.embeddingPiTangent s := by
   intro x hx y _ h
-  simp only [embeddingPiTangent_coe, funext_iff] at h 
+  simp only [embeddingPiTangent_coe, funext_iff] at h
   obtain ⟨h₁, h₂⟩ := Prod.mk.inj_iff.1 (h (f.ind x hx))
-  rw [f.apply_ind x hx] at h₂ 
-  rw [← h₂, f.apply_ind x hx, one_smul, one_smul] at h₁ 
+  rw [f.apply_ind x hx] at h₂
+  rw [← h₂, f.apply_ind x hx, one_smul, one_smul] at h₁
   have := f.mem_extChartAt_source_of_eq_one h₂.symm
   exact (extChartAt I (f.c _)).injOn (f.mem_extChartAt_ind_source x hx) this h₁
 #align smooth_bump_covering.embedding_pi_tangent_inj_on SmoothBumpCovering.embeddingPiTangent_injOn

• 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) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module geometry.manifold.whitney_embedding
-! leanprover-community/mathlib commit 86c29aefdba50b3f33e86e52e3b2f51a0d8f0282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Geometry.Manifold.Diffeomorph
 import Mathlib.Geometry.Manifold.Instances.Real
 import Mathlib.Geometry.Manifold.PartitionOfUnity
 
+#align_import geometry.manifold.whitney_embedding from "leanprover-community/mathlib"@"86c29aefdba50b3f33e86e52e3b2f51a0d8f0282"
+
 /-!
 # Whitney embedding theorem