geometry.manifold.vector_bundle.fiberwise_linear ⟷ Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
 -/
-import Geometry.Manifold.ContMdiff
+import Geometry.Manifold.ContMDiff.Defs
 
 #align_import geometry.manifold.vector_bundle.fiberwise_linear from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
 

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

@@ -150,12 +150,12 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B
           (e.restr (u ×ˢ univ)).EqOnSource
             (FiberwiseLinear.partialHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn) :=
   by
-  rw [SetCoe.forall'] at h 
+  rw [SetCoe.forall'] at h
   -- choose s hs hsp φ u hu hφ h2φ heφ using h,
   -- the following 2 lines should be `choose s hs hsp φ u hu hφ h2φ heφ using h,`
   -- `choose` produces a proof term that takes a long time to type-check by the kernel (it seems)
   -- porting note: todo: try using `choose` again in Lean 4
-  simp only [Classical.skolem, ← exists_prop] at h 
+  simp only [Classical.skolem, ← exists_prop] at h
   rcases h with ⟨s, hs, hsp, φ, u, hu, hφ, h2φ, heφ⟩
   have hesu : ∀ p : e.source, e.source ∩ s p = u p ×ˢ univ :=
     by
@@ -171,7 +171,7 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B
     by
     intro p q hq
     have : q ∈ u p ×ˢ (univ : Set F) := ⟨hq, trivial⟩
-    rw [← hesu p] at this 
+    rw [← hesu p] at this
     exact this.1
   have he : e.source = (Prod.fst '' e.source) ×ˢ (univ : Set F) :=
     by
@@ -219,7 +219,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
       e.EqOnSource (FiberwiseLinear.partialHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
   by
   classical
-  rw [SetCoe.forall'] at h 
+  rw [SetCoe.forall'] at h
   choose! φ u hu hUu hux hφ h2φ heφ using h
   have heuφ : ∀ x : U, eq_on e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) :=
     by
@@ -269,7 +269,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
     intro y hy
     rw [hΦφ ⟨x, hx⟩ y hy]
   refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
-  rw [hU] at hp 
+  rw [hU] at hp
   -- using rw on the next line seems to cause a timeout in kernel type-checking
   refine' (heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩).trans _
   trace

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

@@ -217,11 +217,68 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (Φ x : F →L[𝕜] F)) U) (h2Φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((Φ x).symm : F →L[𝕜] F)) U),
       e.EqOnSource (FiberwiseLinear.partialHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
-  by classical
+  by
+  classical
+  rw [SetCoe.forall'] at h 
+  choose! φ u hu hUu hux hφ h2φ heφ using h
+  have heuφ : ∀ x : U, eq_on e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) :=
+    by
+    intro x p hp
+    refine' (heφ x).2 _
+    rw [(heφ x).1]
+    exact hp
+  have huφ : ∀ (x x' : U) (y : B) (hyx : y ∈ u x) (hyx' : y ∈ u x'), φ x y = φ x' y :=
+    by
+    intro p p' y hyp hyp'
+    ext v
+    have h1 : e (y, v) = (y, φ p y v) := heuφ _ ⟨(id hyp : (y, v).fst ∈ u p), trivial⟩
+    have h2 : e (y, v) = (y, φ p' y v) := heuφ _ ⟨(id hyp' : (y, v).fst ∈ u p'), trivial⟩
+    exact congr_arg Prod.snd (h1.symm.trans h2)
+  have hUu' : U = ⋃ i, u i := by
+    ext x
+    rw [mem_Union]
+    refine' ⟨fun h => ⟨⟨x, h⟩, hux _⟩, _⟩
+    rintro ⟨x, hx⟩
+    exact hUu x hx
+  have hU' : IsOpen U := by
+    rw [hUu']
+    apply isOpen_iUnion hu
+  let Φ₀ : U → F ≃L[𝕜] F := Union_lift u (fun x => φ x ∘ coe) huφ U hUu'.le
+  let Φ : B → F ≃L[𝕜] F := fun y =>
+    if hy : y ∈ U then Φ₀ ⟨y, hy⟩ else ContinuousLinearEquiv.refl 𝕜 F
+  have hΦ : ∀ (y) (hy : y ∈ U), Φ y = Φ₀ ⟨y, hy⟩ := fun y hy => dif_pos hy
+  have hΦφ : ∀ x : U, ∀ y ∈ u x, Φ y = φ x y :=
+    by
+    intro x y hyu
+    refine' (hΦ y (hUu x hyu)).trans _
+    exact Union_lift_mk ⟨y, hyu⟩ _
+  have hΦ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => (Φ y : F →L[𝕜] F)) U :=
+    by
+    apply contMDiffOn_of_locally_contMDiffOn
+    intro x hx
+    refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
+    refine' (ContMDiffOn.congr (hφ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
+    intro y hy
+    rw [hΦφ ⟨x, hx⟩ y hy]
+  have h2Φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => ((Φ y).symm : F →L[𝕜] F)) U :=
+    by
+    apply contMDiffOn_of_locally_contMDiffOn
+    intro x hx
+    refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
+    refine' (ContMDiffOn.congr (h2φ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
+    intro y hy
+    rw [hΦφ ⟨x, hx⟩ y hy]
+  refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
+  rw [hU] at hp 
+  -- using rw on the next line seems to cause a timeout in kernel type-checking
+  refine' (heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩).trans _
+  trace
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr (_, _)]]"
+  rw [hΦφ]
+  apply hux
 #align smooth_fiberwise_linear.locality_aux₂ SmoothFiberwiseLinear.locality_aux₂
 -/
 
--- using rw on the next line seems to cause a timeout in kernel type-checking
 variable (F B IB)
 
 #print smoothFiberwiseLinear /-

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

@@ -217,68 +217,11 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (Φ x : F →L[𝕜] F)) U) (h2Φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((Φ x).symm : F →L[𝕜] F)) U),
       e.EqOnSource (FiberwiseLinear.partialHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
-  by
-  classical
-  rw [SetCoe.forall'] at h 
-  choose! φ u hu hUu hux hφ h2φ heφ using h
-  have heuφ : ∀ x : U, eq_on e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) :=
-    by
-    intro x p hp
-    refine' (heφ x).2 _
-    rw [(heφ x).1]
-    exact hp
-  have huφ : ∀ (x x' : U) (y : B) (hyx : y ∈ u x) (hyx' : y ∈ u x'), φ x y = φ x' y :=
-    by
-    intro p p' y hyp hyp'
-    ext v
-    have h1 : e (y, v) = (y, φ p y v) := heuφ _ ⟨(id hyp : (y, v).fst ∈ u p), trivial⟩
-    have h2 : e (y, v) = (y, φ p' y v) := heuφ _ ⟨(id hyp' : (y, v).fst ∈ u p'), trivial⟩
-    exact congr_arg Prod.snd (h1.symm.trans h2)
-  have hUu' : U = ⋃ i, u i := by
-    ext x
-    rw [mem_Union]
-    refine' ⟨fun h => ⟨⟨x, h⟩, hux _⟩, _⟩
-    rintro ⟨x, hx⟩
-    exact hUu x hx
-  have hU' : IsOpen U := by
-    rw [hUu']
-    apply isOpen_iUnion hu
-  let Φ₀ : U → F ≃L[𝕜] F := Union_lift u (fun x => φ x ∘ coe) huφ U hUu'.le
-  let Φ : B → F ≃L[𝕜] F := fun y =>
-    if hy : y ∈ U then Φ₀ ⟨y, hy⟩ else ContinuousLinearEquiv.refl 𝕜 F
-  have hΦ : ∀ (y) (hy : y ∈ U), Φ y = Φ₀ ⟨y, hy⟩ := fun y hy => dif_pos hy
-  have hΦφ : ∀ x : U, ∀ y ∈ u x, Φ y = φ x y :=
-    by
-    intro x y hyu
-    refine' (hΦ y (hUu x hyu)).trans _
-    exact Union_lift_mk ⟨y, hyu⟩ _
-  have hΦ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => (Φ y : F →L[𝕜] F)) U :=
-    by
-    apply contMDiffOn_of_locally_contMDiffOn
-    intro x hx
-    refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
-    refine' (ContMDiffOn.congr (hφ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
-    intro y hy
-    rw [hΦφ ⟨x, hx⟩ y hy]
-  have h2Φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => ((Φ y).symm : F →L[𝕜] F)) U :=
-    by
-    apply contMDiffOn_of_locally_contMDiffOn
-    intro x hx
-    refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
-    refine' (ContMDiffOn.congr (h2φ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
-    intro y hy
-    rw [hΦφ ⟨x, hx⟩ y hy]
-  refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
-  rw [hU] at hp 
-  -- using rw on the next line seems to cause a timeout in kernel type-checking
-  refine' (heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩).trans _
-  trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr (_, _)]]"
-  rw [hΦφ]
-  apply hux
+  by classical
 #align smooth_fiberwise_linear.locality_aux₂ SmoothFiberwiseLinear.locality_aux₂
 -/
 
+-- using rw on the next line seems to cause a timeout in kernel type-checking
 variable (F B IB)
 
 #print smoothFiberwiseLinear /-

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

@@ -321,7 +321,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     · apply contMDiffOn_const
     · apply contMDiffOn_const
     ·
-      simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_localEquiv,
+      simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_partialEquiv,
         PartialEquiv.refl_source, univ_prod_univ]
     ·
       simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_apply, Prod.mk.eta,

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

@@ -38,10 +38,10 @@ variable {φ φ' : B → F ≃L[𝕜] F} {U U' : Set B}
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print FiberwiseLinear.localHomeomorph /-
+#print FiberwiseLinear.partialHomeomorph /-
 /-- For `B` a topological space and `F` a `𝕜`-normed space, a map from `U : set B` to `F ≃L[𝕜] F`
 determines a local homeomorphism from `B × F` to itself by its action fiberwise. -/
-def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
+def partialHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) : PartialHomeomorph (B × F) (B × F)
     where
@@ -63,54 +63,55 @@ def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
     haveI : ContinuousOn (fun p : B × F => (((φ p.1).symm : F →L[𝕜] F), p.2)) (U ×ˢ univ) :=
       h2φ.prod_map continuousOn_id
     continuous_on_fst.prod (is_bounded_bilinear_map_apply.continuous.comp_continuous_on this)
-#align fiberwise_linear.local_homeomorph FiberwiseLinear.localHomeomorph
+#align fiberwise_linear.local_homeomorph FiberwiseLinear.partialHomeomorph
 -/
 
-#print FiberwiseLinear.trans_localHomeomorph_apply /-
+#print FiberwiseLinear.trans_partialHomeomorph_apply /-
 /-- Compute the composition of two local homeomorphisms induced by fiberwise linear
 equivalences. -/
-theorem trans_localHomeomorph_apply (hU : IsOpen U)
+theorem trans_partialHomeomorph_apply (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) (hU' : IsOpen U')
     (hφ' : ContinuousOn (fun x => φ' x : B → F →L[𝕜] F) U')
     (h2φ' : ContinuousOn (fun x => (φ' x).symm : B → F →L[𝕜] F) U') (b : B) (v : F) :
-    (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ')
+    (FiberwiseLinear.partialHomeomorph φ hU hφ h2φ ≫ₕ
+          FiberwiseLinear.partialHomeomorph φ' hU' hφ' h2φ')
         ⟨b, v⟩ =
       ⟨b, φ' b (φ b v)⟩ :=
   rfl
-#align fiberwise_linear.trans_local_homeomorph_apply FiberwiseLinear.trans_localHomeomorph_apply
+#align fiberwise_linear.trans_local_homeomorph_apply FiberwiseLinear.trans_partialHomeomorph_apply
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print FiberwiseLinear.source_trans_localHomeomorph /-
+#print FiberwiseLinear.source_trans_partialHomeomorph /-
 /-- Compute the source of the composition of two local homeomorphisms induced by fiberwise linear
 equivalences. -/
-theorem source_trans_localHomeomorph (hU : IsOpen U)
+theorem source_trans_partialHomeomorph (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) (hU' : IsOpen U')
     (hφ' : ContinuousOn (fun x => φ' x : B → F →L[𝕜] F) U')
     (h2φ' : ContinuousOn (fun x => (φ' x).symm : B → F →L[𝕜] F) U') :
-    (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ
-          FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ').source =
+    (FiberwiseLinear.partialHomeomorph φ hU hφ h2φ ≫ₕ
+          FiberwiseLinear.partialHomeomorph φ' hU' hφ' h2φ').source =
       (U ∩ U') ×ˢ univ :=
-  by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
-#align fiberwise_linear.source_trans_local_homeomorph FiberwiseLinear.source_trans_localHomeomorph
+  by dsimp only [FiberwiseLinear.partialHomeomorph]; mfld_set_tac
+#align fiberwise_linear.source_trans_local_homeomorph FiberwiseLinear.source_trans_partialHomeomorph
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print FiberwiseLinear.target_trans_localHomeomorph /-
+#print FiberwiseLinear.target_trans_partialHomeomorph /-
 /-- Compute the target of the composition of two local homeomorphisms induced by fiberwise linear
 equivalences. -/
-theorem target_trans_localHomeomorph (hU : IsOpen U)
+theorem target_trans_partialHomeomorph (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) (hU' : IsOpen U')
     (hφ' : ContinuousOn (fun x => φ' x : B → F →L[𝕜] F) U')
     (h2φ' : ContinuousOn (fun x => (φ' x).symm : B → F →L[𝕜] F) U') :
-    (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ
-          FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ').target =
+    (FiberwiseLinear.partialHomeomorph φ hU hφ h2φ ≫ₕ
+          FiberwiseLinear.partialHomeomorph φ' hU' hφ' h2φ').target =
       (U ∩ U') ×ˢ univ :=
-  by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
-#align fiberwise_linear.target_trans_local_homeomorph FiberwiseLinear.target_trans_localHomeomorph
+  by dsimp only [FiberwiseLinear.partialHomeomorph]; mfld_set_tac
+#align fiberwise_linear.target_trans_local_homeomorph FiberwiseLinear.target_trans_partialHomeomorph
 -/
 
 end FiberwiseLinear
@@ -140,14 +141,14 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B
                 SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u) (h2φ :
                 SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
                 (e.restr s).EqOnSource
-                  (FiberwiseLinear.localHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn)) :
+                  (FiberwiseLinear.partialHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn)) :
     ∃ (U : Set B) (hU : e.source = U ×ˢ univ),
       ∀ x ∈ U,
         ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u) (huU : u ⊆ U) (hux : x ∈ u) (hφ :
           SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u) (h2φ :
           SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
           (e.restr (u ×ˢ univ)).EqOnSource
-            (FiberwiseLinear.localHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn) :=
+            (FiberwiseLinear.partialHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn) :=
   by
   rw [SetCoe.forall'] at h 
   -- choose s hs hsp φ u hu hφ h2φ heφ using h,
@@ -211,11 +212,11 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
           SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u) (h2φ :
           SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
           (e.restr (u ×ˢ univ)).EqOnSource
-            (FiberwiseLinear.localHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn)) :
+            (FiberwiseLinear.partialHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn)) :
     ∃ (Φ : B → F ≃L[𝕜] F) (U : Set B) (hU₀ : IsOpen U) (hΦ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (Φ x : F →L[𝕜] F)) U) (h2Φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((Φ x).symm : F →L[𝕜] F)) U),
-      e.EqOnSource (FiberwiseLinear.localHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
+      e.EqOnSource (FiberwiseLinear.partialHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
   by
   classical
   rw [SetCoe.forall'] at h 
@@ -291,7 +292,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-      {e | e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn)}
+      {e | e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn)}
   trans' := by
     simp_rw [mem_Union]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ ⟨φ', U', hU', hφ', h2φ', heφ'⟩
@@ -306,8 +307,8 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
           (fun x : B => (φ x).symm.toContinuousLinearMap ∘L (φ' x).symm.toContinuousLinearMap)
           (U ∩ U')
       exact (h2φ.mono <| inter_subset_left _ _).clm_comp (h2φ'.mono <| inter_subset_right _ _)
-    · apply FiberwiseLinear.source_trans_localHomeomorph
-    · rintro ⟨b, v⟩ hb; apply FiberwiseLinear.trans_localHomeomorph_apply
+    · apply FiberwiseLinear.source_trans_partialHomeomorph
+    · rintro ⟨b, v⟩ hb; apply FiberwiseLinear.trans_partialHomeomorph_apply
   symm' := by
     simp_rw [mem_Union]
     rintro e ⟨φ, U, hU, hφ, h2φ, heφ⟩
@@ -320,11 +321,11 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     · apply contMDiffOn_const
     · apply contMDiffOn_const
     ·
-      simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_localEquiv,
+      simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_localEquiv,
         PartialEquiv.refl_source, univ_prod_univ]
     ·
-      simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_apply, Prod.mk.eta, id.def,
-        ContinuousLinearEquiv.coe_refl', PartialHomeomorph.mk_coe, PartialEquiv.coe_mk]
+      simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_apply, Prod.mk.eta,
+        id.def, ContinuousLinearEquiv.coe_refl', PartialHomeomorph.mk_coe, PartialEquiv.coe_mk]
   locality' :=
     by
     -- the hard work has been extracted to `locality_aux₁` and `locality_aux₂`
@@ -346,7 +347,7 @@ theorem mem_smoothFiberwiseLinear_iff (e : PartialHomeomorph (B × F) (B × F))
       ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-        e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
+        e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
   show e ∈ Set.iUnion _ ↔ _ by simp only [mem_Union]; rfl
 #align mem_smooth_fiberwise_linear_iff mem_smoothFiberwiseLinear_iff
 -/

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

@@ -321,10 +321,10 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     · apply contMDiffOn_const
     ·
       simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_localEquiv,
-        LocalEquiv.refl_source, univ_prod_univ]
+        PartialEquiv.refl_source, univ_prod_univ]
     ·
       simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_apply, Prod.mk.eta, id.def,
-        ContinuousLinearEquiv.coe_refl', PartialHomeomorph.mk_coe, LocalEquiv.coe_mk]
+        ContinuousLinearEquiv.coe_refl', PartialHomeomorph.mk_coe, PartialEquiv.coe_mk]
   locality' :=
     by
     -- the hard work has been extracted to `locality_aux₁` and `locality_aux₂`

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

@@ -43,7 +43,7 @@ variable {φ φ' : B → F ≃L[𝕜] F} {U U' : Set B}
 determines a local homeomorphism from `B × F` to itself by its action fiberwise. -/
 def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
-    (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) : LocalHomeomorph (B × F) (B × F)
+    (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) : PartialHomeomorph (B × F) (B × F)
     where
   toFun x := (x.1, φ x.1 x.2)
   invFun x := (x.1, (φ x.1).symm x.2)
@@ -130,7 +130,7 @@ local homeomorphism.
 Then the source of `e` is of the form `U ×ˢ univ`, for some set `U` in `B`, and, at any point `x` in
 `U`, admits a neighbourhood `u` of `x` such that `e` is equal on `u ×ˢ univ` to some bi-smooth
 fiberwise linear local homeomorphism. -/
-theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B × F))
+theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B × F))
     (h :
       ∀ p ∈ e.source,
         ∃ s : Set (B × F),
@@ -203,7 +203,7 @@ together the various bi-smooth fiberwise linear local homeomorphism which exist
 
 The `U` in the conclusion is the same `U` as in the hypothesis. We state it like this, because this
 is exactly what we need for `smooth_fiberwise_linear`. -/
-theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B × F)) (U : Set B)
+theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B × F)) (U : Set B)
     (hU : e.source = U ×ˢ univ)
     (h :
       ∀ x ∈ U,
@@ -320,11 +320,11 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     · apply contMDiffOn_const
     · apply contMDiffOn_const
     ·
-      simp only [FiberwiseLinear.localHomeomorph, LocalHomeomorph.refl_localEquiv,
+      simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_localEquiv,
         LocalEquiv.refl_source, univ_prod_univ]
     ·
-      simp only [FiberwiseLinear.localHomeomorph, LocalHomeomorph.refl_apply, Prod.mk.eta, id.def,
-        ContinuousLinearEquiv.coe_refl', LocalHomeomorph.mk_coe, LocalEquiv.coe_mk]
+      simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_apply, Prod.mk.eta, id.def,
+        ContinuousLinearEquiv.coe_refl', PartialHomeomorph.mk_coe, LocalEquiv.coe_mk]
   locality' :=
     by
     -- the hard work has been extracted to `locality_aux₁` and `locality_aux₂`
@@ -341,7 +341,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
 
 #print mem_smoothFiberwiseLinear_iff /-
 @[simp]
-theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
+theorem mem_smoothFiberwiseLinear_iff (e : PartialHomeomorph (B × F) (B × F)) :
     e ∈ smoothFiberwiseLinear B F IB ↔
       ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
 -/
-import Mathbin.Geometry.Manifold.ContMdiff
+import Geometry.Manifold.ContMdiff
 
 #align_import geometry.manifold.vector_bundle.fiberwise_linear from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
-
-! This file was ported from Lean 3 source module geometry.manifold.vector_bundle.fiberwise_linear
-! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Manifold.ContMdiff
 
+#align_import geometry.manifold.vector_bundle.fiberwise_linear from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
+
 /-! # The groupoid of smooth, fiberwise-linear maps
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module geometry.manifold.vector_bundle.fiberwise_linear
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.Geometry.Manifold.ContMdiff
 
 /-! # The groupoid of smooth, fiberwise-linear maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains preliminaries for the definition of a smooth vector bundle: an associated
 `structure_groupoid`, the groupoid of `smooth_fiberwise_linear` functions.
 -/

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

@@ -38,6 +38,7 @@ variable {φ φ' : B → F ≃L[𝕜] F} {U U' : Set B}
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberwiseLinear.localHomeomorph /-
 /-- For `B` a topological space and `F` a `𝕜`-normed space, a map from `U : set B` to `F ≃L[𝕜] F`
 determines a local homeomorphism from `B × F` to itself by its action fiberwise. -/
 def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
@@ -63,7 +64,9 @@ def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
       h2φ.prod_map continuousOn_id
     continuous_on_fst.prod (is_bounded_bilinear_map_apply.continuous.comp_continuous_on this)
 #align fiberwise_linear.local_homeomorph FiberwiseLinear.localHomeomorph
+-/
 
+#print FiberwiseLinear.trans_localHomeomorph_apply /-
 /-- Compute the composition of two local homeomorphisms induced by fiberwise linear
 equivalences. -/
 theorem trans_localHomeomorph_apply (hU : IsOpen U)
@@ -76,8 +79,10 @@ theorem trans_localHomeomorph_apply (hU : IsOpen U)
       ⟨b, φ' b (φ b v)⟩ :=
   rfl
 #align fiberwise_linear.trans_local_homeomorph_apply FiberwiseLinear.trans_localHomeomorph_apply
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberwiseLinear.source_trans_localHomeomorph /-
 /-- Compute the source of the composition of two local homeomorphisms induced by fiberwise linear
 equivalences. -/
 theorem source_trans_localHomeomorph (hU : IsOpen U)
@@ -90,8 +95,10 @@ theorem source_trans_localHomeomorph (hU : IsOpen U)
       (U ∩ U') ×ˢ univ :=
   by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
 #align fiberwise_linear.source_trans_local_homeomorph FiberwiseLinear.source_trans_localHomeomorph
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberwiseLinear.target_trans_localHomeomorph /-
 /-- Compute the target of the composition of two local homeomorphisms induced by fiberwise linear
 equivalences. -/
 theorem target_trans_localHomeomorph (hU : IsOpen U)
@@ -104,6 +111,7 @@ theorem target_trans_localHomeomorph (hU : IsOpen U)
       (U ∩ U') ×ˢ univ :=
   by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
 #align fiberwise_linear.target_trans_local_homeomorph FiberwiseLinear.target_trans_localHomeomorph
+-/
 
 end FiberwiseLinear
 
@@ -115,6 +123,7 @@ variable {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print SmoothFiberwiseLinear.locality_aux₁ /-
 /-- Let `e` be a local homeomorphism of `B × F`.  Suppose that at every point `p` in the source of
 `e`, there is some neighbourhood `s` of `p` on which `e` is equal to a bi-smooth fiberwise linear
 local homeomorphism.
@@ -176,11 +185,13 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B 
   · intro y hy; refine' ⟨(y, 0), heu ⟨p, hp⟩ ⟨_, _⟩ hy, rfl⟩
   · rw [← hesu, e.restr_source_inter]; exact heφ ⟨p, hp⟩
 #align smooth_fiberwise_linear.locality_aux₁ SmoothFiberwiseLinear.locality_aux₁
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr (_, _)]] -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print SmoothFiberwiseLinear.locality_aux₂ /-
 /-- Let `e` be a local homeomorphism of `B × F` whose source is `U ×ˢ univ`, for some set `U` in
 `B`, and which, at any point `x` in `U`, admits a neighbourhood `u` of `x` such that `e` is equal on
 `u ×ˢ univ` to some bi-smooth fiberwise linear local homeomorphism.  Then `e` itself is equal to
@@ -265,9 +276,11 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
   rw [hΦφ]
   apply hux
 #align smooth_fiberwise_linear.locality_aux₂ SmoothFiberwiseLinear.locality_aux₂
+-/
 
 variable (F B IB)
 
+#print smoothFiberwiseLinear /-
 /-- For `B` a manifold and `F` a normed space, the groupoid on `B × F` consisting of local
 homeomorphisms which are bi-smooth and fiberwise linear, and induce the identity on `B`.
 When a (topological) vector bundle is smooth, then the composition of charts associated
@@ -324,7 +337,9 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ hee'
     exact ⟨φ, U, hU, hφ, h2φ, Setoid.trans hee' heφ⟩
 #align smooth_fiberwise_linear smoothFiberwiseLinear
+-/
 
+#print mem_smoothFiberwiseLinear_iff /-
 @[simp]
 theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
     e ∈ smoothFiberwiseLinear B F IB ↔
@@ -334,4 +349,5 @@ theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
         e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
   show e ∈ Set.iUnion _ ↔ _ by simp only [mem_Union]; rfl
 #align mem_smooth_fiberwise_linear_iff mem_smoothFiberwiseLinear_iff
+-/
 

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

@@ -242,18 +242,18 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
     exact Union_lift_mk ⟨y, hyu⟩ _
   have hΦ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => (Φ y : F →L[𝕜] F)) U :=
     by
-    apply contMdiffOn_of_locally_contMdiffOn
+    apply contMDiffOn_of_locally_contMDiffOn
     intro x hx
     refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
-    refine' (ContMdiffOn.congr (hφ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
+    refine' (ContMDiffOn.congr (hφ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
     intro y hy
     rw [hΦφ ⟨x, hx⟩ y hy]
   have h2Φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => ((Φ y).symm : F →L[𝕜] F)) U :=
     by
-    apply contMdiffOn_of_locally_contMdiffOn
+    apply contMDiffOn_of_locally_contMDiffOn
     intro x hx
     refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
-    refine' (ContMdiffOn.congr (h2φ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
+    refine' (ContMDiffOn.congr (h2φ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
     intro y hy
     rw [hΦφ ⟨x, hx⟩ y hy]
   refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
@@ -304,8 +304,8 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
   id_mem' := by
     simp_rw [mem_Union]
     refine' ⟨fun b => ContinuousLinearEquiv.refl 𝕜 F, univ, isOpen_univ, _, _, ⟨_, fun b hb => _⟩⟩
-    · apply contMdiffOn_const
-    · apply contMdiffOn_const
+    · apply contMDiffOn_const
+    · apply contMDiffOn_const
     ·
       simp only [FiberwiseLinear.localHomeomorph, LocalHomeomorph.refl_localEquiv,
         LocalEquiv.refl_source, univ_prod_univ]

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

@@ -207,63 +207,63 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
       e.EqOnSource (FiberwiseLinear.localHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
   by
   classical
-    rw [SetCoe.forall'] at h 
-    choose! φ u hu hUu hux hφ h2φ heφ using h
-    have heuφ : ∀ x : U, eq_on e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) :=
-      by
-      intro x p hp
-      refine' (heφ x).2 _
-      rw [(heφ x).1]
-      exact hp
-    have huφ : ∀ (x x' : U) (y : B) (hyx : y ∈ u x) (hyx' : y ∈ u x'), φ x y = φ x' y :=
-      by
-      intro p p' y hyp hyp'
-      ext v
-      have h1 : e (y, v) = (y, φ p y v) := heuφ _ ⟨(id hyp : (y, v).fst ∈ u p), trivial⟩
-      have h2 : e (y, v) = (y, φ p' y v) := heuφ _ ⟨(id hyp' : (y, v).fst ∈ u p'), trivial⟩
-      exact congr_arg Prod.snd (h1.symm.trans h2)
-    have hUu' : U = ⋃ i, u i := by
-      ext x
-      rw [mem_Union]
-      refine' ⟨fun h => ⟨⟨x, h⟩, hux _⟩, _⟩
-      rintro ⟨x, hx⟩
-      exact hUu x hx
-    have hU' : IsOpen U := by
-      rw [hUu']
-      apply isOpen_iUnion hu
-    let Φ₀ : U → F ≃L[𝕜] F := Union_lift u (fun x => φ x ∘ coe) huφ U hUu'.le
-    let Φ : B → F ≃L[𝕜] F := fun y =>
-      if hy : y ∈ U then Φ₀ ⟨y, hy⟩ else ContinuousLinearEquiv.refl 𝕜 F
-    have hΦ : ∀ (y) (hy : y ∈ U), Φ y = Φ₀ ⟨y, hy⟩ := fun y hy => dif_pos hy
-    have hΦφ : ∀ x : U, ∀ y ∈ u x, Φ y = φ x y :=
-      by
-      intro x y hyu
-      refine' (hΦ y (hUu x hyu)).trans _
-      exact Union_lift_mk ⟨y, hyu⟩ _
-    have hΦ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => (Φ y : F →L[𝕜] F)) U :=
-      by
-      apply contMdiffOn_of_locally_contMdiffOn
-      intro x hx
-      refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
-      refine' (ContMdiffOn.congr (hφ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
-      intro y hy
-      rw [hΦφ ⟨x, hx⟩ y hy]
-    have h2Φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => ((Φ y).symm : F →L[𝕜] F)) U :=
-      by
-      apply contMdiffOn_of_locally_contMdiffOn
-      intro x hx
-      refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
-      refine' (ContMdiffOn.congr (h2φ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
-      intro y hy
-      rw [hΦφ ⟨x, hx⟩ y hy]
-    refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
-    rw [hU] at hp 
-    -- using rw on the next line seems to cause a timeout in kernel type-checking
-    refine' (heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩).trans _
-    trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr (_, _)]]"
-    rw [hΦφ]
-    apply hux
+  rw [SetCoe.forall'] at h 
+  choose! φ u hu hUu hux hφ h2φ heφ using h
+  have heuφ : ∀ x : U, eq_on e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) :=
+    by
+    intro x p hp
+    refine' (heφ x).2 _
+    rw [(heφ x).1]
+    exact hp
+  have huφ : ∀ (x x' : U) (y : B) (hyx : y ∈ u x) (hyx' : y ∈ u x'), φ x y = φ x' y :=
+    by
+    intro p p' y hyp hyp'
+    ext v
+    have h1 : e (y, v) = (y, φ p y v) := heuφ _ ⟨(id hyp : (y, v).fst ∈ u p), trivial⟩
+    have h2 : e (y, v) = (y, φ p' y v) := heuφ _ ⟨(id hyp' : (y, v).fst ∈ u p'), trivial⟩
+    exact congr_arg Prod.snd (h1.symm.trans h2)
+  have hUu' : U = ⋃ i, u i := by
+    ext x
+    rw [mem_Union]
+    refine' ⟨fun h => ⟨⟨x, h⟩, hux _⟩, _⟩
+    rintro ⟨x, hx⟩
+    exact hUu x hx
+  have hU' : IsOpen U := by
+    rw [hUu']
+    apply isOpen_iUnion hu
+  let Φ₀ : U → F ≃L[𝕜] F := Union_lift u (fun x => φ x ∘ coe) huφ U hUu'.le
+  let Φ : B → F ≃L[𝕜] F := fun y =>
+    if hy : y ∈ U then Φ₀ ⟨y, hy⟩ else ContinuousLinearEquiv.refl 𝕜 F
+  have hΦ : ∀ (y) (hy : y ∈ U), Φ y = Φ₀ ⟨y, hy⟩ := fun y hy => dif_pos hy
+  have hΦφ : ∀ x : U, ∀ y ∈ u x, Φ y = φ x y :=
+    by
+    intro x y hyu
+    refine' (hΦ y (hUu x hyu)).trans _
+    exact Union_lift_mk ⟨y, hyu⟩ _
+  have hΦ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => (Φ y : F →L[𝕜] F)) U :=
+    by
+    apply contMdiffOn_of_locally_contMdiffOn
+    intro x hx
+    refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
+    refine' (ContMdiffOn.congr (hφ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
+    intro y hy
+    rw [hΦφ ⟨x, hx⟩ y hy]
+  have h2Φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun y => ((Φ y).symm : F →L[𝕜] F)) U :=
+    by
+    apply contMdiffOn_of_locally_contMdiffOn
+    intro x hx
+    refine' ⟨u ⟨x, hx⟩, hu ⟨x, hx⟩, hux _, _⟩
+    refine' (ContMdiffOn.congr (h2φ ⟨x, hx⟩) _).mono (inter_subset_right _ _)
+    intro y hy
+    rw [hΦφ ⟨x, hx⟩ y hy]
+  refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
+  rw [hU] at hp 
+  -- using rw on the next line seems to cause a timeout in kernel type-checking
+  refine' (heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩).trans _
+  trace
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr (_, _)]]"
+  rw [hΦφ]
+  apply hux
 #align smooth_fiberwise_linear.locality_aux₂ SmoothFiberwiseLinear.locality_aux₂
 
 variable (F B IB)
@@ -278,7 +278,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-      { e | e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) }
+      {e | e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn)}
   trans' := by
     simp_rw [mem_Union]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ ⟨φ', U', hU', hφ', h2φ', heφ'⟩

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

@@ -127,25 +127,25 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B 
         ∃ s : Set (B × F),
           IsOpen s ∧
             p ∈ s ∧
-              ∃ (φ : B → F ≃L[𝕜] F)(u : Set B)(hu : IsOpen u)(hφ :
-                SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)(h2φ :
+              ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u) (hφ :
+                SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u) (h2φ :
                 SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
                 (e.restr s).EqOnSource
                   (FiberwiseLinear.localHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn)) :
-    ∃ (U : Set B)(hU : e.source = U ×ˢ univ),
+    ∃ (U : Set B) (hU : e.source = U ×ˢ univ),
       ∀ x ∈ U,
-        ∃ (φ : B → F ≃L[𝕜] F)(u : Set B)(hu : IsOpen u)(huU : u ⊆ U)(hux : x ∈ u)(hφ :
-          SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)(h2φ :
+        ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u) (huU : u ⊆ U) (hux : x ∈ u) (hφ :
+          SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u) (h2φ :
           SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
           (e.restr (u ×ˢ univ)).EqOnSource
             (FiberwiseLinear.localHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn) :=
   by
-  rw [SetCoe.forall'] at h
+  rw [SetCoe.forall'] at h 
   -- choose s hs hsp φ u hu hφ h2φ heφ using h,
   -- the following 2 lines should be `choose s hs hsp φ u hu hφ h2φ heφ using h,`
   -- `choose` produces a proof term that takes a long time to type-check by the kernel (it seems)
   -- porting note: todo: try using `choose` again in Lean 4
-  simp only [Classical.skolem, ← exists_prop] at h
+  simp only [Classical.skolem, ← exists_prop] at h 
   rcases h with ⟨s, hs, hsp, φ, u, hu, hφ, h2φ, heφ⟩
   have hesu : ∀ p : e.source, e.source ∩ s p = u p ×ˢ univ :=
     by
@@ -161,7 +161,7 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B 
     by
     intro p q hq
     have : q ∈ u p ×ˢ (univ : Set F) := ⟨hq, trivial⟩
-    rw [← hesu p] at this
+    rw [← hesu p] at this 
     exact this.1
   have he : e.source = (Prod.fst '' e.source) ×ˢ (univ : Set F) :=
     by
@@ -196,18 +196,18 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
     (hU : e.source = U ×ˢ univ)
     (h :
       ∀ x ∈ U,
-        ∃ (φ : B → F ≃L[𝕜] F)(u : Set B)(hu : IsOpen u)(hUu : u ⊆ U)(hux : x ∈ u)(hφ :
-          SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)(h2φ :
+        ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u) (hUu : u ⊆ U) (hux : x ∈ u) (hφ :
+          SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u) (h2φ :
           SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
           (e.restr (u ×ˢ univ)).EqOnSource
             (FiberwiseLinear.localHomeomorph φ hu hφ.ContinuousOn h2φ.ContinuousOn)) :
-    ∃ (Φ : B → F ≃L[𝕜] F)(U : Set B)(hU₀ : IsOpen U)(hΦ :
-      SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (Φ x : F →L[𝕜] F)) U)(h2Φ :
+    ∃ (Φ : B → F ≃L[𝕜] F) (U : Set B) (hU₀ : IsOpen U) (hΦ :
+      SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (Φ x : F →L[𝕜] F)) U) (h2Φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((Φ x).symm : F →L[𝕜] F)) U),
       e.EqOnSource (FiberwiseLinear.localHomeomorph Φ hU₀ hΦ.ContinuousOn h2Φ.ContinuousOn) :=
   by
   classical
-    rw [SetCoe.forall'] at h
+    rw [SetCoe.forall'] at h 
     choose! φ u hu hUu hux hφ h2φ heφ using h
     have heuφ : ∀ x : U, eq_on e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) :=
       by
@@ -257,7 +257,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
       intro y hy
       rw [hΦφ ⟨x, hx⟩ y hy]
     refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
-    rw [hU] at hp
+    rw [hU] at hp 
     -- using rw on the next line seems to cause a timeout in kernel type-checking
     refine' (heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩).trans _
     trace
@@ -328,8 +328,8 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
 @[simp]
 theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
     e ∈ smoothFiberwiseLinear B F IB ↔
-      ∃ (φ : B → F ≃L[𝕜] F)(U : Set B)(hU : IsOpen U)(hφ :
-        SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)(h2φ :
+      ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
+        SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
         e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
   show e ∈ Set.iUnion _ ↔ _ by simp only [mem_Union]; rfl

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

@@ -311,7 +311,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
         LocalEquiv.refl_source, univ_prod_univ]
     ·
       simp only [FiberwiseLinear.localHomeomorph, LocalHomeomorph.refl_apply, Prod.mk.eta, id.def,
-        ContinuousLinearEquiv.coe_refl', LocalHomeomorph.mk_coe, [anonymous]]
+        ContinuousLinearEquiv.coe_refl', LocalHomeomorph.mk_coe, LocalEquiv.coe_mk]
   locality' :=
     by
     -- the hard work has been extracted to `locality_aux₁` and `locality_aux₂`

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

@@ -21,7 +21,7 @@ noncomputable section
 
 open Set TopologicalSpace
 
-open Manifold Topology
+open scoped Manifold Topology
 
 /-! ### The groupoid of smooth, fiberwise-linear maps -/
 

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

@@ -88,9 +88,7 @@ theorem source_trans_localHomeomorph (hU : IsOpen U)
     (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ
           FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ').source =
       (U ∩ U') ×ˢ univ :=
-  by
-  dsimp only [FiberwiseLinear.localHomeomorph]
-  mfld_set_tac
+  by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
 #align fiberwise_linear.source_trans_local_homeomorph FiberwiseLinear.source_trans_localHomeomorph
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -104,9 +102,7 @@ theorem target_trans_localHomeomorph (hU : IsOpen U)
     (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ
           FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ').target =
       (U ∩ U') ×ˢ univ :=
-  by
-  dsimp only [FiberwiseLinear.localHomeomorph]
-  mfld_set_tac
+  by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
 #align fiberwise_linear.target_trans_local_homeomorph FiberwiseLinear.target_trans_localHomeomorph
 
 end FiberwiseLinear
@@ -177,10 +173,8 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B 
   refine' ⟨Prod.fst '' e.source, he, _⟩
   rintro x ⟨p, hp, rfl⟩
   refine' ⟨φ ⟨p, hp⟩, u ⟨p, hp⟩, hu ⟨p, hp⟩, _, hu' _, hφ ⟨p, hp⟩, h2φ ⟨p, hp⟩, _⟩
-  · intro y hy
-    refine' ⟨(y, 0), heu ⟨p, hp⟩ ⟨_, _⟩ hy, rfl⟩
-  · rw [← hesu, e.restr_source_inter]
-    exact heφ ⟨p, hp⟩
+  · intro y hy; refine' ⟨(y, 0), heu ⟨p, hp⟩ ⟨_, _⟩ hy, rfl⟩
+  · rw [← hesu, e.restr_source_inter]; exact heφ ⟨p, hp⟩
 #align smooth_fiberwise_linear.locality_aux₁ SmoothFiberwiseLinear.locality_aux₁
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -300,8 +294,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
           (U ∩ U')
       exact (h2φ.mono <| inter_subset_left _ _).clm_comp (h2φ'.mono <| inter_subset_right _ _)
     · apply FiberwiseLinear.source_trans_localHomeomorph
-    · rintro ⟨b, v⟩ hb
-      apply FiberwiseLinear.trans_localHomeomorph_apply
+    · rintro ⟨b, v⟩ hb; apply FiberwiseLinear.trans_localHomeomorph_apply
   symm' := by
     simp_rw [mem_Union]
     rintro e ⟨φ, U, hU, hφ, h2φ, heφ⟩
@@ -339,8 +332,6 @@ theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)(h2φ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
         e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
-  show e ∈ Set.iUnion _ ↔ _ by
-    simp only [mem_Union]
-    rfl
+  show e ∈ Set.iUnion _ ↔ _ by simp only [mem_Union]; rfl
 #align mem_smooth_fiberwise_linear_iff mem_smoothFiberwiseLinear_iff
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -236,7 +236,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
       exact hUu x hx
     have hU' : IsOpen U := by
       rw [hUu']
-      apply isOpen_unionᵢ hu
+      apply isOpen_iUnion hu
     let Φ₀ : U → F ≃L[𝕜] F := Union_lift u (fun x => φ x ∘ coe) huφ U hUu'.le
     let Φ : B → F ≃L[𝕜] F := fun y =>
       if hy : y ∈ U then Φ₀ ⟨y, hy⟩ else ContinuousLinearEquiv.refl 𝕜 F
@@ -339,7 +339,7 @@ theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)(h2φ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
         e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
-  show e ∈ Set.unionᵢ _ ↔ _ by
+  show e ∈ Set.iUnion _ ↔ _ by
     simp only [mem_Union]
     rfl
 #align mem_smooth_fiberwise_linear_iff mem_smoothFiberwiseLinear_iff

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -3,19 +3,17 @@ Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
 
-! This file was ported from Lean 3 source module geometry.manifold.vector_bundle
-! leanprover-community/mathlib commit 87ecf9614fedda186a792c38ee571904f548df29
+! This file was ported from Lean 3 source module geometry.manifold.vector_bundle.fiberwise_linear
+! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Manifold.ContMdiff
 
-/-! # Smooth vector bundles
+/-! # The groupoid of smooth, fiberwise-linear maps
 
-This file will eventually contain the definition of a smooth vector bundle. For now, it contains
-preliminaries regarding an associated `structure_groupoid`, the groupoid of
-`smooth_fiberwise_linear` functions. When a (topological) vector bundle is smooth, then the
-composition of charts associated to the vector bundle belong to this groupoid.
+This file contains preliminaries for the definition of a smooth vector bundle: an associated
+`structure_groupoid`, the groupoid of `smooth_fiberwise_linear` functions.
 -/
 
 
@@ -124,7 +122,6 @@ variable {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type
 /-- Let `e` be a local homeomorphism of `B × F`.  Suppose that at every point `p` in the source of
 `e`, there is some neighbourhood `s` of `p` on which `e` is equal to a bi-smooth fiberwise linear
 local homeomorphism.
-
 Then the source of `e` is of the form `U ×ˢ univ`, for some set `U` in `B`, and, at any point `x` in
 `U`, admits a neighbourhood `u` of `x` such that `e` is equal on `u ×ˢ univ` to some bi-smooth
 fiberwise linear local homeomorphism. -/
@@ -335,3 +332,15 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F)
     exact ⟨φ, U, hU, hφ, h2φ, Setoid.trans hee' heφ⟩
 #align smooth_fiberwise_linear smoothFiberwiseLinear
 
+@[simp]
+theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
+    e ∈ smoothFiberwiseLinear B F IB ↔
+      ∃ (φ : B → F ≃L[𝕜] F)(U : Set B)(hU : IsOpen U)(hφ :
+        SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)(h2φ :
+        SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
+        e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.ContinuousOn h2φ.ContinuousOn) :=
+  show e ∈ Set.unionᵢ _ ↔ _ by
+    simp only [mem_Union]
+    rfl
+#align mem_smooth_fiberwise_linear_iff mem_smoothFiberwiseLinear_iff
+

In all cases, the original proof fixed itself.

@@ -221,21 +221,6 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
   apply hux
 #align smooth_fiberwise_linear.locality_aux₂ SmoothFiberwiseLinear.locality_aux₂
 
-/- Porting note: `simp only [mem_iUnion]` fails in the next definition. This aux lemma is a
-workaround. -/
-private theorem mem_aux {e : PartialHomeomorph (B × F) (B × F)} :
-    (e ∈ ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
-      (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
-      (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-        {e | e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn
-          h2φ.continuousOn)}) ↔
-      ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
-        (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
-        (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-          e.EqOnSource
-            (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn h2φ.continuousOn) := by
-  simp only [mem_iUnion, mem_setOf_eq]
-
 variable (F B IB)
 
 /-- For `B` a manifold and `F` a normed space, the groupoid on `B × F` consisting of local
@@ -249,7 +234,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
       (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
         {e | e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn h2φ.continuousOn)}
   trans' := by
-    simp only [mem_aux]
+    simp only [mem_iUnion]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ ⟨φ', U', hU', hφ', h2φ', heφ'⟩
     refine' ⟨fun b => (φ b).trans (φ' b), _, hU.inter hU', _, _,
       Setoid.trans (PartialHomeomorph.EqOnSource.trans' heφ heφ') ⟨_, _⟩⟩
@@ -272,27 +257,38 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     simp_rw [ContinuousLinearEquiv.symm_symm]
     exact hφ
   id_mem' := by
-    /- porting note: `simp_rw [mem_iUnion]` failed; expanding. Was:
     simp_rw [mem_iUnion]
-    refine' ⟨fun b => ContinuousLinearEquiv.refl 𝕜 F, univ, isOpen_univ, _, _, ⟨_, fun b hb => _⟩⟩
-    -/
-    refine mem_iUnion.2 ⟨fun _ ↦ .refl 𝕜 F, mem_iUnion.2 ⟨univ, mem_iUnion.2 ⟨isOpen_univ, ?_⟩⟩⟩
-    refine mem_iUnion.2 ⟨contMDiffOn_const, mem_iUnion.2 ⟨contMDiffOn_const, ?_, ?_⟩⟩
-    · simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_partialEquiv,
-        PartialEquiv.refl_source, univ_prod_univ]
-    · exact eqOn_refl id _
+    refine ⟨fun _ ↦ ContinuousLinearEquiv.refl 𝕜 F, univ, isOpen_univ, smoothOn_const,
+      smoothOn_const, ⟨?_, fun b _hb ↦ rfl⟩⟩
+    simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_partialEquiv,
+      PartialEquiv.refl_source, univ_prod_univ]
   locality' := by
     -- the hard work has been extracted to `locality_aux₁` and `locality_aux₂`
-    simp only [mem_aux]
+    simp only [mem_iUnion]
     intro e he
     obtain ⟨U, hU, h⟩ := SmoothFiberwiseLinear.locality_aux₁ e he
     exact SmoothFiberwiseLinear.locality_aux₂ e U hU h
   mem_of_eqOnSource' := by
-    simp only [mem_aux]
+    simp only [mem_iUnion]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ hee'
     exact ⟨φ, U, hU, hφ, h2φ, Setoid.trans hee' heφ⟩
 #align smooth_fiberwise_linear smoothFiberwiseLinear
 
+variable {F B IB} in
+-- TODO: can this be inlined into the next lemma?
+private theorem mem_aux {e : PartialHomeomorph (B × F) (B × F)} :
+    (e ∈ ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
+      (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
+      (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
+        {e | e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn
+          h2φ.continuousOn)}) ↔
+      ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
+        (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
+        (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
+          e.EqOnSource
+            (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn h2φ.continuousOn) := by
+  simp only [mem_iUnion, mem_setOf_eq]
+
 @[simp]
 theorem mem_smoothFiberwiseLinear_iff (e : PartialHomeomorph (B × F) (B × F)) :
     e ∈ smoothFiberwiseLinear B F IB ↔

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)

@@ -23,7 +23,6 @@ open scoped Manifold Topology
 
 
 variable {𝕜 B F : Type*} [TopologicalSpace B]
-
 variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 namespace FiberwiseLinear

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -265,7 +265,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
       exact (h2φ.mono <| inter_subset_left _ _).clm_comp (h2φ'.mono <| inter_subset_right _ _)
     · apply FiberwiseLinear.source_trans_partialHomeomorph
     · rintro ⟨b, v⟩ -; apply FiberwiseLinear.trans_partialHomeomorph_apply
-  -- porting note: without introducing `e` first, the first `simp only` fails
+  -- Porting note: without introducing `e` first, the first `simp only` fails
   symm' := fun e ↦ by
     simp only [mem_iUnion]
     rintro ⟨φ, U, hU, hφ, h2φ, heφ⟩

Since it refers to PartialEquiv.EqOnSource, the correct naming scheme should not be snake case eq_on_source. I also added mem_of_ because that's the target of the lemma, while EqOnSource is just a hypothesis.

There are no added lemmas or docstrings in this PR. It's all just renaming.

@@ -288,7 +288,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     intro e he
     obtain ⟨U, hU, h⟩ := SmoothFiberwiseLinear.locality_aux₁ e he
     exact SmoothFiberwiseLinear.locality_aux₂ e U hU h
-  eq_on_source' := by
+  mem_of_eqOnSource' := by
     simp only [mem_aux]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ hee'
     exact ⟨φ, U, hU, hφ, h2φ, Setoid.trans hee' heφ⟩

@@ -279,7 +279,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     -/
     refine mem_iUnion.2 ⟨fun _ ↦ .refl 𝕜 F, mem_iUnion.2 ⟨univ, mem_iUnion.2 ⟨isOpen_univ, ?_⟩⟩⟩
     refine mem_iUnion.2 ⟨contMDiffOn_const, mem_iUnion.2 ⟨contMDiffOn_const, ?_, ?_⟩⟩
-    · simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_localEquiv,
+    · simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_partialEquiv,
         PartialEquiv.refl_source, univ_prod_univ]
     · exact eqOn_refl id _
   locality' := by

Follow-up to #8982; a few lemma names were still wrong.

Co-authored-by: Winston Yin <winstonyin@gmail.com>

@@ -31,8 +31,8 @@ namespace FiberwiseLinear
 variable {φ φ' : B → F ≃L[𝕜] F} {U U' : Set B}
 
 /-- For `B` a topological space and `F` a `𝕜`-normed space, a map from `U : Set B` to `F ≃L[𝕜] F`
-determines a local homeomorphism from `B × F` to itself by its action fiberwise. -/
-def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
+determines a partial homeomorphism from `B × F` to itself by its action fiberwise. -/
+def partialHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) :
     PartialHomeomorph (B × F) (B × F) where
@@ -54,71 +54,72 @@ def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
     haveI : ContinuousOn (fun p : B × F => (((φ p.1).symm : F →L[𝕜] F), p.2)) (U ×ˢ univ) :=
       h2φ.prod_map continuousOn_id
     continuousOn_fst.prod (isBoundedBilinearMap_apply.continuous.comp_continuousOn this)
-#align fiberwise_linear.local_homeomorph FiberwiseLinear.localHomeomorph
+#align fiberwise_linear.local_homeomorph FiberwiseLinear.partialHomeomorph
 
-/-- Compute the composition of two local homeomorphisms induced by fiberwise linear
+/-- Compute the composition of two partial homeomorphisms induced by fiberwise linear
 equivalences. -/
-theorem trans_localHomeomorph_apply (hU : IsOpen U)
+theorem trans_partialHomeomorph_apply (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) (hU' : IsOpen U')
     (hφ' : ContinuousOn (fun x => φ' x : B → F →L[𝕜] F) U')
     (h2φ' : ContinuousOn (fun x => (φ' x).symm : B → F →L[𝕜] F) U') (b : B) (v : F) :
-    (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ')
+    (FiberwiseLinear.partialHomeomorph φ hU hφ h2φ ≫ₕ
+      FiberwiseLinear.partialHomeomorph φ' hU' hφ' h2φ')
         ⟨b, v⟩ =
       ⟨b, φ' b (φ b v)⟩ :=
   rfl
-#align fiberwise_linear.trans_local_homeomorph_apply FiberwiseLinear.trans_localHomeomorph_apply
+#align fiberwise_linear.trans_local_homeomorph_apply FiberwiseLinear.trans_partialHomeomorph_apply
 
-/-- Compute the source of the composition of two local homeomorphisms induced by fiberwise linear
+/-- Compute the source of the composition of two partial homeomorphisms induced by fiberwise linear
 equivalences. -/
-theorem source_trans_localHomeomorph (hU : IsOpen U)
+theorem source_trans_partialHomeomorph (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) (hU' : IsOpen U')
     (hφ' : ContinuousOn (fun x => φ' x : B → F →L[𝕜] F) U')
     (h2φ' : ContinuousOn (fun x => (φ' x).symm : B → F →L[𝕜] F) U') :
-    (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ
-          FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ').source =
+    (FiberwiseLinear.partialHomeomorph φ hU hφ h2φ ≫ₕ
+          FiberwiseLinear.partialHomeomorph φ' hU' hφ' h2φ').source =
       (U ∩ U') ×ˢ univ :=
-  by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
-#align fiberwise_linear.source_trans_local_homeomorph FiberwiseLinear.source_trans_localHomeomorph
+  by dsimp only [FiberwiseLinear.partialHomeomorph]; mfld_set_tac
+#align fiberwise_linear.source_trans_local_homeomorph FiberwiseLinear.source_trans_partialHomeomorph
 
-/-- Compute the target of the composition of two local homeomorphisms induced by fiberwise linear
+/-- Compute the target of the composition of two partial homeomorphisms induced by fiberwise linear
 equivalences. -/
-theorem target_trans_localHomeomorph (hU : IsOpen U)
+theorem target_trans_partialHomeomorph (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) (hU' : IsOpen U')
     (hφ' : ContinuousOn (fun x => φ' x : B → F →L[𝕜] F) U')
     (h2φ' : ContinuousOn (fun x => (φ' x).symm : B → F →L[𝕜] F) U') :
-    (FiberwiseLinear.localHomeomorph φ hU hφ h2φ ≫ₕ
-          FiberwiseLinear.localHomeomorph φ' hU' hφ' h2φ').target =
+    (FiberwiseLinear.partialHomeomorph φ hU hφ h2φ ≫ₕ
+          FiberwiseLinear.partialHomeomorph φ' hU' hφ' h2φ').target =
       (U ∩ U') ×ˢ univ :=
-  by dsimp only [FiberwiseLinear.localHomeomorph]; mfld_set_tac
-#align fiberwise_linear.target_trans_local_homeomorph FiberwiseLinear.target_trans_localHomeomorph
+  by dsimp only [FiberwiseLinear.partialHomeomorph]; mfld_set_tac
+#align fiberwise_linear.target_trans_local_homeomorph FiberwiseLinear.target_trans_partialHomeomorph
 
 end FiberwiseLinear
 
 variable {EB : Type*} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type*}
   [TopologicalSpace HB] [ChartedSpace HB B] {IB : ModelWithCorners 𝕜 EB HB}
 
-/-- Let `e` be a local homeomorphism of `B × F`.  Suppose that at every point `p` in the source of
+/-- Let `e` be a partial homeomorphism of `B × F`.  Suppose that at every point `p` in the source of
 `e`, there is some neighbourhood `s` of `p` on which `e` is equal to a bi-smooth fiberwise linear
-local homeomorphism.
+partial homeomorphism.
 Then the source of `e` is of the form `U ×ˢ univ`, for some set `U` in `B`, and, at any point `x` in
 `U`, admits a neighbourhood `u` of `x` such that `e` is equal on `u ×ˢ univ` to some bi-smooth
-fiberwise linear local homeomorphism. -/
+fiberwise linear partial homeomorphism. -/
 theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B × F))
     (h : ∀ p ∈ e.source, ∃ s : Set (B × F), IsOpen s ∧ p ∈ s ∧
       ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u)
         (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)
         (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
           (e.restr s).EqOnSource
-            (FiberwiseLinear.localHomeomorph φ hu hφ.continuousOn h2φ.continuousOn)) :
+            (FiberwiseLinear.partialHomeomorph φ hu hφ.continuousOn h2φ.continuousOn)) :
     ∃ U : Set B, e.source = U ×ˢ univ ∧ ∀ x ∈ U,
         ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u) (_huU : u ⊆ U) (_hux : x ∈ u),
           ∃ (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)
             (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
             (e.restr (u ×ˢ univ)).EqOnSource
-              (FiberwiseLinear.localHomeomorph φ hu hφ.continuousOn h2φ.continuousOn) := by
+              (FiberwiseLinear.partialHomeomorph φ hu hφ.continuousOn h2φ.continuousOn) := by
   rw [SetCoe.forall'] at h
   choose s hs hsp φ u hu hφ h2φ heφ using h
   have hesu : ∀ p : e.source, e.source ∩ s p = u p ×ˢ univ := by
@@ -147,14 +148,14 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B
   · rw [← hesu, e.restr_source_inter]; exact heφ ⟨p, hp⟩
 #align smooth_fiberwise_linear.locality_aux₁ SmoothFiberwiseLinear.locality_aux₁
 
-/-- Let `e` be a local homeomorphism of `B × F` whose source is `U ×ˢ univ`, for some set `U` in
-`B`, and which, at any point `x` in `U`, admits a neighbourhood `u` of `x` such that `e` is equal on
-`u ×ˢ univ` to some bi-smooth fiberwise linear local homeomorphism.  Then `e` itself is equal to
-some bi-smooth fiberwise linear local homeomorphism.
+/-- Let `e` be a partial homeomorphism of `B × F` whose source is `U ×ˢ univ`, for some set `U` in
+`B`, and which, at any point `x` in `U`, admits a neighbourhood `u` of `x` such that `e` is equal
+on `u ×ˢ univ` to some bi-smooth fiberwise linear partial homeomorphism.  Then `e` itself
+is equal to some bi-smooth fiberwise linear partial homeomorphism.
 
 This is the key mathematical point of the `locality` condition in the construction of the
-`StructureGroupoid` of bi-smooth fiberwise linear local homeomorphisms.  The proof is by gluing
-together the various bi-smooth fiberwise linear local homeomorphism which exist locally.
+`StructureGroupoid` of bi-smooth fiberwise linear partial homeomorphisms.  The proof is by gluing
+together the various bi-smooth fiberwise linear partial homeomorphism which exist locally.
 
 The `U` in the conclusion is the same `U` as in the hypothesis. We state it like this, because this
 is exactly what we need for `smoothFiberwiseLinear`. -/
@@ -165,11 +166,11 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B
         (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)
         (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
           (e.restr (u ×ˢ univ)).EqOnSource
-            (FiberwiseLinear.localHomeomorph φ hu hφ.continuousOn h2φ.continuousOn)) :
+            (FiberwiseLinear.partialHomeomorph φ hu hφ.continuousOn h2φ.continuousOn)) :
     ∃ (Φ : B → F ≃L[𝕜] F) (U : Set B) (hU₀ : IsOpen U) (hΦ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (Φ x : F →L[𝕜] F)) U) (h2Φ :
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((Φ x).symm : F →L[𝕜] F)) U),
-      e.EqOnSource (FiberwiseLinear.localHomeomorph Φ hU₀ hΦ.continuousOn h2Φ.continuousOn) := by
+      e.EqOnSource (FiberwiseLinear.partialHomeomorph Φ hU₀ hΦ.continuousOn h2Φ.continuousOn) := by
   classical
   rw [SetCoe.forall'] at h
   choose! φ u hu hUu hux hφ h2φ heφ using h
@@ -227,12 +228,13 @@ private theorem mem_aux {e : PartialHomeomorph (B × F) (B × F)} :
     (e ∈ ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
       (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
       (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-        {e | e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.continuousOn
+        {e | e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn
           h2φ.continuousOn)}) ↔
       ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
         (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
         (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-          e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.continuousOn h2φ.continuousOn) := by
+          e.EqOnSource
+            (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn h2φ.continuousOn) := by
   simp only [mem_iUnion, mem_setOf_eq]
 
 variable (F B IB)
@@ -246,7 +248,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
       (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
       (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-        {e | e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.continuousOn h2φ.continuousOn)}
+        {e | e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn h2φ.continuousOn)}
   trans' := by
     simp only [mem_aux]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ ⟨φ', U', hU', hφ', h2φ', heφ'⟩
@@ -261,8 +263,8 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
           (fun x : B => (φ x).symm.toContinuousLinearMap ∘L (φ' x).symm.toContinuousLinearMap)
           (U ∩ U')
       exact (h2φ.mono <| inter_subset_left _ _).clm_comp (h2φ'.mono <| inter_subset_right _ _)
-    · apply FiberwiseLinear.source_trans_localHomeomorph
-    · rintro ⟨b, v⟩ -; apply FiberwiseLinear.trans_localHomeomorph_apply
+    · apply FiberwiseLinear.source_trans_partialHomeomorph
+    · rintro ⟨b, v⟩ -; apply FiberwiseLinear.trans_partialHomeomorph_apply
   -- porting note: without introducing `e` first, the first `simp only` fails
   symm' := fun e ↦ by
     simp only [mem_iUnion]
@@ -277,7 +279,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     -/
     refine mem_iUnion.2 ⟨fun _ ↦ .refl 𝕜 F, mem_iUnion.2 ⟨univ, mem_iUnion.2 ⟨isOpen_univ, ?_⟩⟩⟩
     refine mem_iUnion.2 ⟨contMDiffOn_const, mem_iUnion.2 ⟨contMDiffOn_const, ?_, ?_⟩⟩
-    · simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_localEquiv,
+    · simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_localEquiv,
         PartialEquiv.refl_source, univ_prod_univ]
     · exact eqOn_refl id _
   locality' := by
@@ -298,6 +300,6 @@ theorem mem_smoothFiberwiseLinear_iff (e : PartialHomeomorph (B × F) (B × F))
       ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
-        e.EqOnSource (FiberwiseLinear.localHomeomorph φ hU hφ.continuousOn h2φ.continuousOn) :=
+        e.EqOnSource (FiberwiseLinear.partialHomeomorph φ hU hφ.continuousOn h2φ.continuousOn) :=
   mem_aux
 #align mem_smooth_fiberwise_linear_iff mem_smoothFiberwiseLinear_iff

The current name is misleading: there's no open set involved; it's just an equivalence between subsets of domain and target. zulip discussion

PEquiv is similarly named: this is fine, as they're different designs for the same concept.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -278,7 +278,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     refine mem_iUnion.2 ⟨fun _ ↦ .refl 𝕜 F, mem_iUnion.2 ⟨univ, mem_iUnion.2 ⟨isOpen_univ, ?_⟩⟩⟩
     refine mem_iUnion.2 ⟨contMDiffOn_const, mem_iUnion.2 ⟨contMDiffOn_const, ?_, ?_⟩⟩
     · simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_localEquiv,
-        LocalEquiv.refl_source, univ_prod_univ]
+        PartialEquiv.refl_source, univ_prod_univ]
     · exact eqOn_refl id _
   locality' := by
     -- the hard work has been extracted to `locality_aux₁` and `locality_aux₂`

LocalHomeomorph evokes a "local homeomorphism": this is not what this means. Instead, this is a homeomorphism on an open set of the domain (extended to the whole space, by the junk value pattern). Hence, partial homeomorphism is more appropriate, and avoids confusion with IsLocallyHomeomorph.

A future PR will rename LocalEquiv to PartialEquiv.

Zulip discussion

@@ -35,7 +35,7 @@ determines a local homeomorphism from `B × F` to itself by its action fiberwise
 def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
     (hφ : ContinuousOn (fun x => φ x : B → F →L[𝕜] F) U)
     (h2φ : ContinuousOn (fun x => (φ x).symm : B → F →L[𝕜] F) U) :
-    LocalHomeomorph (B × F) (B × F) where
+    PartialHomeomorph (B × F) (B × F) where
   toFun x := (x.1, φ x.1 x.2)
   invFun x := (x.1, (φ x.1).symm x.2)
   source := U ×ˢ univ
@@ -106,7 +106,7 @@ local homeomorphism.
 Then the source of `e` is of the form `U ×ˢ univ`, for some set `U` in `B`, and, at any point `x` in
 `U`, admits a neighbourhood `u` of `x` such that `e` is equal on `u ×ˢ univ` to some bi-smooth
 fiberwise linear local homeomorphism. -/
-theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B × F))
+theorem SmoothFiberwiseLinear.locality_aux₁ (e : PartialHomeomorph (B × F) (B × F))
     (h : ∀ p ∈ e.source, ∃ s : Set (B × F), IsOpen s ∧ p ∈ s ∧
       ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u)
         (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x : F →L[𝕜] F)) u)
@@ -158,7 +158,7 @@ together the various bi-smooth fiberwise linear local homeomorphism which exist
 
 The `U` in the conclusion is the same `U` as in the hypothesis. We state it like this, because this
 is exactly what we need for `smoothFiberwiseLinear`. -/
-theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B × F)) (U : Set B)
+theorem SmoothFiberwiseLinear.locality_aux₂ (e : PartialHomeomorph (B × F) (B × F)) (U : Set B)
     (hU : e.source = U ×ˢ univ)
     (h : ∀ x ∈ U,
       ∃ (φ : B → F ≃L[𝕜] F) (u : Set B) (hu : IsOpen u) (_hUu : u ⊆ U) (_hux : x ∈ u)
@@ -223,7 +223,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
 
 /- Porting note: `simp only [mem_iUnion]` fails in the next definition. This aux lemma is a
 workaround. -/
-private theorem mem_aux {e : LocalHomeomorph (B × F) (B × F)} :
+private theorem mem_aux {e : PartialHomeomorph (B × F) (B × F)} :
     (e ∈ ⋃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U)
       (hφ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U)
       (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => (φ x).symm : B → F →L[𝕜] F) U),
@@ -251,7 +251,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     simp only [mem_aux]
     rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ ⟨φ', U', hU', hφ', h2φ', heφ'⟩
     refine' ⟨fun b => (φ b).trans (φ' b), _, hU.inter hU', _, _,
-      Setoid.trans (LocalHomeomorph.EqOnSource.trans' heφ heφ') ⟨_, _⟩⟩
+      Setoid.trans (PartialHomeomorph.EqOnSource.trans' heφ heφ') ⟨_, _⟩⟩
     · show
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F)
           (fun x : B => (φ' x).toContinuousLinearMap ∘L (φ x).toContinuousLinearMap) (U ∩ U')
@@ -267,7 +267,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
   symm' := fun e ↦ by
     simp only [mem_iUnion]
     rintro ⟨φ, U, hU, hφ, h2φ, heφ⟩
-    refine' ⟨fun b => (φ b).symm, U, hU, h2φ, _, LocalHomeomorph.EqOnSource.symm' heφ⟩
+    refine' ⟨fun b => (φ b).symm, U, hU, h2φ, _, PartialHomeomorph.EqOnSource.symm' heφ⟩
     simp_rw [ContinuousLinearEquiv.symm_symm]
     exact hφ
   id_mem' := by
@@ -277,7 +277,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     -/
     refine mem_iUnion.2 ⟨fun _ ↦ .refl 𝕜 F, mem_iUnion.2 ⟨univ, mem_iUnion.2 ⟨isOpen_univ, ?_⟩⟩⟩
     refine mem_iUnion.2 ⟨contMDiffOn_const, mem_iUnion.2 ⟨contMDiffOn_const, ?_, ?_⟩⟩
-    · simp only [FiberwiseLinear.localHomeomorph, LocalHomeomorph.refl_localEquiv,
+    · simp only [FiberwiseLinear.localHomeomorph, PartialHomeomorph.refl_localEquiv,
         LocalEquiv.refl_source, univ_prod_univ]
     · exact eqOn_refl id _
   locality' := by
@@ -293,7 +293,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
 #align smooth_fiberwise_linear smoothFiberwiseLinear
 
 @[simp]
-theorem mem_smoothFiberwiseLinear_iff (e : LocalHomeomorph (B × F) (B × F)) :
+theorem mem_smoothFiberwiseLinear_iff (e : PartialHomeomorph (B × F) (B × F)) :
     e ∈ smoothFiberwiseLinear B F IB ↔
       ∃ (φ : B → F ≃L[𝕜] F) (U : Set B) (hU : IsOpen U) (hφ :
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => φ x : B → F →L[𝕜] F) U) (h2φ :

They have type ContinuousOn ..., hence should be named accordingly. Suggested by @fpvandoorn in #8736.

@@ -46,11 +46,11 @@ def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
   right_inv' _ _ := Prod.ext rfl (ContinuousLinearEquiv.apply_symm_apply _ _)
   open_source := hU.prod isOpen_univ
   open_target := hU.prod isOpen_univ
-  continuous_toFun :=
+  continuousOn_toFun :=
     have : ContinuousOn (fun p : B × F => ((φ p.1 : F →L[𝕜] F), p.2)) (U ×ˢ univ) :=
       hφ.prod_map continuousOn_id
     continuousOn_fst.prod (isBoundedBilinearMap_apply.continuous.comp_continuousOn this)
-  continuous_invFun :=
+  continuousOn_invFun :=
     haveI : ContinuousOn (fun p : B × F => (((φ p.1).symm : F →L[𝕜] F), p.2)) (U ×ˢ univ) :=
       h2φ.prod_map continuousOn_id
     continuousOn_fst.prod (isBoundedBilinearMap_apply.continuous.comp_continuousOn this)

At about 2200 lines, this is currently the longest file in the Geometry/Manifolds.

(It also moves the slowly compiling proof of ContMDiffWithinAt.cle_arrowCongr out of a common recompilation path.)

@@ -3,7 +3,7 @@ Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
 -/
-import Mathlib.Geometry.Manifold.ContMDiff
+import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace
 
 #align_import geometry.manifold.vector_bundle.fiberwise_linear from "leanprover-community/mathlib"@"be2c24f56783935652cefffb4bfca7e4b25d167e"
 

@@ -49,11 +49,11 @@ def localHomeomorph (φ : B → F ≃L[𝕜] F) (hU : IsOpen U)
   continuous_toFun :=
     have : ContinuousOn (fun p : B × F => ((φ p.1 : F →L[𝕜] F), p.2)) (U ×ˢ univ) :=
       hφ.prod_map continuousOn_id
-    continuousOn_fst.prod (isBoundedBilinearMapApply.continuous.comp_continuousOn this)
+    continuousOn_fst.prod (isBoundedBilinearMap_apply.continuous.comp_continuousOn this)
   continuous_invFun :=
     haveI : ContinuousOn (fun p : B × F => (((φ p.1).symm : F →L[𝕜] F), p.2)) (U ×ˢ univ) :=
       h2φ.prod_map continuousOn_id
-    continuousOn_fst.prod (isBoundedBilinearMapApply.continuous.comp_continuousOn this)
+    continuousOn_fst.prod (isBoundedBilinearMap_apply.continuous.comp_continuousOn this)
 #align fiberwise_linear.local_homeomorph FiberwiseLinear.localHomeomorph
 
 /-- Compute the composition of two local homeomorphisms induced by fiberwise linear

Adds a term elaborator for congr(...) "congruence quotations". For example, if hf : f = f' and hx : x = x', then we have congr($hf $x) : f x = f' x'. This supports the functions having implicit arguments, and it has support for subsingleton instance arguments. So for example, if s t : Set X are sets with Fintype instances and h : s = t then congr(Fintype.card $h) : Fintype.card s = Fintype.card t works.

Ports the congrm tactic as a convenient frontend for applying a congruence quotation to the goal. Holes are turned into congruence holes. For example, congrm 1 + ?_ uses congr(1 + $(?_)). Placeholders (_) do not turn into congruence holes; that's not to say they have to be identical on the LHS and RHS, but congrm itself is responsible for finding a congruence lemma for such arguments.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>

@@ -216,8 +216,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
   refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
   rw [hU] at hp
   rw [heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩]
-  -- porting note: replaced `congrm` with manual `congr_arg`
-  refine congr_arg (Prod.mk _) ?_
+  congrm (_, ?_)
   rw [hΦφ]
   apply hux
 #align smooth_fiberwise_linear.locality_aux₂ SmoothFiberwiseLinear.locality_aux₂

@@ -119,7 +119,7 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B 
             (h2φ : SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((φ x).symm : F →L[𝕜] F)) u),
             (e.restr (u ×ˢ univ)).EqOnSource
               (FiberwiseLinear.localHomeomorph φ hu hφ.continuousOn h2φ.continuousOn) := by
-  rw [SetCoe.forall'] at h 
+  rw [SetCoe.forall'] at h
   choose s hs hsp φ u hu hφ h2φ heφ using h
   have hesu : ∀ p : e.source, e.source ∩ s p = u p ×ˢ univ := by
     intro p
@@ -132,7 +132,7 @@ theorem SmoothFiberwiseLinear.locality_aux₁ (e : LocalHomeomorph (B × F) (B 
   have heu : ∀ p : e.source, ∀ q : B × F, q.fst ∈ u p → q ∈ e.source := by
     intro p q hq
     have : q ∈ u p ×ˢ (univ : Set F) := ⟨hq, trivial⟩
-    rw [← hesu p] at this 
+    rw [← hesu p] at this
     exact this.1
   have he : e.source = (Prod.fst '' e.source) ×ˢ (univ : Set F) := by
     apply HasSubset.Subset.antisymm
@@ -171,7 +171,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun x => ((Φ x).symm : F →L[𝕜] F)) U),
       e.EqOnSource (FiberwiseLinear.localHomeomorph Φ hU₀ hΦ.continuousOn h2Φ.continuousOn) := by
   classical
-  rw [SetCoe.forall'] at h 
+  rw [SetCoe.forall'] at h
   choose! φ u hu hUu hux hφ h2φ heφ using h
   have heuφ : ∀ x : U, EqOn e (fun q => (q.1, φ x q.1 q.2)) (u x ×ˢ univ) := fun x p hp ↦ by
     refine' (heφ x).2 _
@@ -214,7 +214,7 @@ theorem SmoothFiberwiseLinear.locality_aux₂ (e : LocalHomeomorph (B × F) (B 
     intro y hy
     rw [hΦφ ⟨x, hx⟩ y hy]
   refine' ⟨Φ, U, hU', hΦ, h2Φ, hU, fun p hp => _⟩
-  rw [hU] at hp 
+  rw [hU] at hp
   rw [heuφ ⟨p.fst, hp.1⟩ ⟨hux _, hp.2⟩]
   -- porting note: replaced `congrm` with manual `congr_arg`
   refine congr_arg (Prod.mk _) ?_

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

This has nice performance benefits.

@@ -22,7 +22,7 @@ open scoped Manifold Topology
 /-! ### The groupoid of smooth, fiberwise-linear maps -/
 
 
-variable {𝕜 B F : Type _} [TopologicalSpace B]
+variable {𝕜 B F : Type*} [TopologicalSpace B]
 
 variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
@@ -97,7 +97,7 @@ theorem target_trans_localHomeomorph (hU : IsOpen U)
 
 end FiberwiseLinear
 
-variable {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type _}
+variable {EB : Type*} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type*}
   [TopologicalSpace HB] [ChartedSpace HB B] {IB : ModelWithCorners 𝕜 EB HB}
 
 /-- Let `e` be a local homeomorphism of `B × F`.  Suppose that at every point `p` in the source of

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Heather Macbeth
-
-! This file was ported from Lean 3 source module geometry.manifold.vector_bundle.fiberwise_linear
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Geometry.Manifold.ContMDiff
 
+#align_import geometry.manifold.vector_bundle.fiberwise_linear from "leanprover-community/mathlib"@"be2c24f56783935652cefffb4bfca7e4b25d167e"
+
 /-! # The groupoid of smooth, fiberwise-linear maps
 
 This file contains preliminaries for the definition of a smooth vector bundle: an associated