geometry.manifold.vector_bundle.basic ⟷ Mathlib.Geometry.Manifold.VectorBundle.Basic

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

@@ -471,7 +471,7 @@ namespace VectorPrebundle
 variable [∀ x, TopologicalSpace (E x)] {F E}
 
 #print VectorPrebundle.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
 /-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
 class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
   exists_smooth_coord_change :

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

@@ -226,7 +226,7 @@ theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π F E) :=
   simp_rw [(· ∘ ·), FiberBundle.extChartAt]
   apply cont_diff_within_at_fst.congr
   · rintro ⟨a, b⟩ hab
-    simp only [mfld_simps] at hab 
+    simp only [mfld_simps] at hab
     have : ((chart_at HB x.1).symm (IB.symm a), b) ∈ (trivialization_at F E x.proj).target := by
       simp only [hab, mfld_simps]
     simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
@@ -364,7 +364,7 @@ instance : SmoothManifoldWithCorners (IB.Prod 𝓘(𝕜, F)) (TotalSpace F E) :=
   by
   refine' { StructureGroupoid.HasGroupoid.comp (smoothFiberwiseLinear B F IB) _ with }
   intro e he
-  rw [mem_smoothFiberwiseLinear_iff] at he 
+  rw [mem_smoothFiberwiseLinear_iff] at he
   obtain ⟨φ, U, hU, hφ, h2φ, heφ⟩ := he
   rw [isLocalStructomorphOn_contDiffGroupoid_iff]
   refine' ⟨ContMDiffOn.congr _ heφ.eq_on, ContMDiffOn.congr _ heφ.symm'.eq_on⟩

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

@@ -383,7 +383,7 @@ namespace VectorBundleCore
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
 #print VectorBundleCore.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coordChangeL :

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

@@ -351,7 +351,7 @@ instance : HasGroupoid (TotalSpace F E) (smoothFiberwiseLinear B F IB)
       · infer_instance
       · infer_instance
     ·
-      simp only [e.symm_trans_source_eq e', FiberwiseLinear.localHomeomorph, trans_to_local_equiv,
+      simp only [e.symm_trans_source_eq e', FiberwiseLinear.partialHomeomorph, trans_to_local_equiv,
         symm_to_local_equiv]
     · rintro ⟨b, v⟩ hb
       have hb' : b ∈ e.base_set ∩ e'.base_set := by

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

@@ -383,7 +383,7 @@ namespace VectorBundleCore
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
 #print VectorBundleCore.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coordChangeL :

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

@@ -148,11 +148,11 @@ variable [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 #print FiberBundle.extChartAt /-
 protected theorem FiberBundle.extChartAt (x : TotalSpace F E) :
     extChartAt (IB.Prod 𝓘(𝕜, F)) x =
-      (trivializationAt F E x.proj).toLocalEquiv ≫
-        (extChartAt IB x.proj).Prod (LocalEquiv.refl F) :=
+      (trivializationAt F E x.proj).toPartialEquiv ≫
+        (extChartAt IB x.proj).Prod (PartialEquiv.refl F) :=
   by
   simp_rw [extChartAt, FiberBundle.chartedSpace_chartAt, extend]
-  simp only [LocalEquiv.trans_assoc, mfld_simps]
+  simp only [PartialEquiv.trans_assoc, mfld_simps]
 #align fiber_bundle.ext_chart_at FiberBundle.extChartAt
 -/
 
@@ -177,9 +177,9 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x
   simp (config := { singlePass := true }) only [contMDiffWithinAt_iff_target]
   rw [and_and_and_comm, ← continuous_within_at_total_space, and_congr_right_iff]
   intro hf
-  simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp, LocalEquiv.trans_apply,
-    LocalEquiv.prod_coe, LocalEquiv.refl_coe, extChartAt_self_apply, modelWithCornersSelf_coe,
-    id_def]
+  simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp,
+    PartialEquiv.trans_apply, PartialEquiv.prod_coe, PartialEquiv.refl_coe, extChartAt_self_apply,
+    modelWithCornersSelf_coe, id_def]
   refine' (contMDiffWithinAt_prod_iff _).trans _
   -- rw doesn't do this?
   have h1 : (fun x => (f x).proj) ⁻¹' (trivialization_at F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=

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

@@ -64,7 +64,7 @@ fields, they can also be C^k vector bundles, etc.
 
 assert_not_exists mfderiv
 
-open Bundle Set LocalHomeomorph
+open Bundle Set PartialHomeomorph
 
 open Function (id_def)
 
@@ -87,8 +87,8 @@ variable [TopologicalSpace F] [TopologicalSpace (TotalSpace F E)] [∀ x, Topolo
 `B × F`. -/
 instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace F E)
     where
-  atlas := (fun e : Trivialization F (π F E) => e.toLocalHomeomorph) '' trivializationAtlas F E
-  chartAt x := (trivializationAt F E x.proj).toLocalHomeomorph
+  atlas := (fun e : Trivialization F (π F E) => e.toPartialHomeomorph) '' trivializationAtlas F E
+  chartAt x := (trivializationAt F E x.proj).toPartialHomeomorph
   mem_chart_source x :=
     (trivializationAt F E x.proj).mem_source.mpr (mem_baseSet_trivializationAt F E x.proj)
   chart_mem_atlas x := mem_image_of_mem _ (trivialization_mem_atlas F E _)
@@ -112,8 +112,8 @@ end
 #print FiberBundle.chartedSpace_chartAt /-
 theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace F E) :
     chartAt (ModelProd HB F) x =
-      (trivializationAt F E x.proj).toLocalHomeomorph ≫ₕ
-        (chartAt HB x.proj).Prod (LocalHomeomorph.refl F) :=
+      (trivializationAt F E x.proj).toPartialHomeomorph ≫ₕ
+        (chartAt HB x.proj).Prod (PartialHomeomorph.refl F) :=
   by
   dsimp only [FiberBundle.chartedSpace, ChartedSpace.comp, FiberBundle.chartedSpace',
     prodChartedSpace, chartedSpaceSelf]
@@ -188,7 +188,7 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x
   refine'
     and_congr (eventually_eq.cont_mdiff_within_at_iff (eventually_of_mem h1 fun x hx => _) _)
       Iff.rfl
-  · simp_rw [Function.comp, LocalHomeomorph.coe_coe, Trivialization.coe_coe]
+  · simp_rw [Function.comp, PartialHomeomorph.coe_coe, Trivialization.coe_coe]
     rw [Trivialization.coe_fst']
     exact hx
   · simp only [mfld_simps]

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

@@ -3,8 +3,8 @@ 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.VectorBundle.FiberwiseLinear
-import Mathbin.Topology.VectorBundle.Constructions
+import Geometry.Manifold.VectorBundle.FiberwiseLinear
+import Topology.VectorBundle.Constructions
 
 #align_import geometry.manifold.vector_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
 
@@ -383,7 +383,7 @@ namespace VectorBundleCore
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
 #print VectorBundleCore.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coordChangeL :
@@ -471,7 +471,7 @@ namespace VectorPrebundle
 variable [∀ x, TopologicalSpace (E x)] {F E}
 
 #print VectorPrebundle.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
 /-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
 class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
   exists_smooth_coord_change :

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

@@ -2,15 +2,12 @@
 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.basic
-! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Manifold.VectorBundle.FiberwiseLinear
 import Mathbin.Topology.VectorBundle.Constructions
 
+#align_import geometry.manifold.vector_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-! # Smooth vector bundles
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
@@ -474,7 +471,7 @@ namespace VectorPrebundle
 variable [∀ x, TopologicalSpace (E x)] {F E}
 
 #print VectorPrebundle.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
 /-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
 class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
   exists_smooth_coord_change :

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

@@ -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.basic
-! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -82,15 +82,15 @@ variable {𝕜 B B' F M : Type _} {E : B → Type _}
 
 section
 
-variable [TopologicalSpace F] [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
+variable [TopologicalSpace F] [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)]
   {HB : Type _} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
 #print FiberBundle.chartedSpace' /-
 /-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
 `B × F`. -/
-instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace E)
+instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace F E)
     where
-  atlas := (fun e : Trivialization F (π E) => e.toLocalHomeomorph) '' trivializationAtlas F E
+  atlas := (fun e : Trivialization F (π F E) => e.toLocalHomeomorph) '' trivializationAtlas F E
   chartAt x := (trivializationAt F E x.proj).toLocalHomeomorph
   mem_chart_source x :=
     (trivializationAt F E x.proj).mem_source.mpr (mem_baseSet_trivializationAt F E x.proj)
@@ -105,7 +105,7 @@ attribute [local reducible] ModelProd
 #print FiberBundle.chartedSpace /-
 /-- Let `B` be a charted space modelled on `HB`.  Then a fiber bundle `E` over a base `B` with model
 fiber `F` is naturally a charted space modelled on `HB.prod F`. -/
-instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace E) :=
+instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace F E) :=
   ChartedSpace.comp _ (ModelProd B F) _
 #align fiber_bundle.charted_space' FiberBundle.chartedSpace
 -/
@@ -113,7 +113,7 @@ instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace E)
 end
 
 #print FiberBundle.chartedSpace_chartAt /-
-theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
+theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace F E) :
     chartAt (ModelProd HB F) x =
       (trivializationAt F E x.proj).toLocalHomeomorph ≫ₕ
         (chartAt HB x.proj).Prod (LocalHomeomorph.refl F) :=
@@ -125,7 +125,7 @@ theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
 -/
 
 #print FiberBundle.chartedSpace_chartAt_symm_fst /-
-theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace E) (y : ModelProd HB F)
+theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace F E) (y : ModelProd HB F)
     (hy : y ∈ (chartAt (ModelProd HB F) x).target) :
     ((chartAt (ModelProd HB F) x).symm y).proj = (chartAt HB x.proj).symm y.1 :=
   by
@@ -139,7 +139,7 @@ end
 section
 
 variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-  [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)] {EB : Type _}
+  [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)] {EB : Type _}
   [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type _} [TopologicalSpace HB]
   (IB : ModelWithCorners 𝕜 EB HB) (E' : B → Type _) [∀ x, Zero (E' x)] {EM : Type _}
   [NormedAddCommGroup EM] [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM]
@@ -149,7 +149,7 @@ variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜
 variable [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
 #print FiberBundle.extChartAt /-
-protected theorem FiberBundle.extChartAt (x : TotalSpace E) :
+protected theorem FiberBundle.extChartAt (x : TotalSpace F E) :
     extChartAt (IB.Prod 𝓘(𝕜, F)) x =
       (trivializationAt F E x.proj).toLocalEquiv ≫
         (extChartAt IB x.proj).Prod (LocalEquiv.refl F) :=
@@ -172,7 +172,7 @@ variable {F E IB}
 
 #print Bundle.contMDiffWithinAt_totalSpace /-
 /-- Characterization of C^n functions into a smooth vector bundle. -/
-theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀ : M} :
+theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x₀ : M} :
     ContMDiffWithinAt IM (IB.Prod 𝓘(𝕜, F)) n f s x₀ ↔
       ContMDiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
         ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) s x₀ :=
@@ -200,7 +200,7 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀
 
 #print Bundle.contMDiffAt_totalSpace /-
 /-- Characterization of C^n functions into a smooth vector bundle. -/
-theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
+theorem contMDiffAt_totalSpace (f : M → TotalSpace F E) (x₀ : M) :
     ContMDiffAt IM (IB.Prod 𝓘(𝕜, F)) n f x₀ ↔
       ContMDiffAt IM IB n (fun x => (f x).proj) x₀ ∧
         ContMDiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ :=
@@ -211,8 +211,9 @@ theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
 #print Bundle.contMDiffAt_section /-
 /-- Characterization of C^n sections of a smooth vector bundle. -/
 theorem contMDiffAt_section (s : ∀ x, E x) (x₀ : B) :
-    ContMDiffAt IB (IB.Prod 𝓘(𝕜, F)) n (fun x => totalSpaceMk x (s x)) x₀ ↔
-      ContMDiffAt IB 𝓘(𝕜, F) n (fun x => (trivializationAt F E x₀ (totalSpaceMk x (s x))).2) x₀ :=
+    ContMDiffAt IB (IB.Prod 𝓘(𝕜, F)) n (fun x => (total_space.mk' F) x (s x)) x₀ ↔
+      ContMDiffAt IB 𝓘(𝕜, F) n (fun x => (trivializationAt F E x₀ ((total_space.mk' F) x (s x))).2)
+        x₀ :=
   by simp_rw [cont_mdiff_at_total_space, and_iff_right_iff_imp]; intro x; exact contMDiffAt_id
 #align bundle.cont_mdiff_at_section Bundle.contMDiffAt_section
 -/
@@ -220,7 +221,7 @@ theorem contMDiffAt_section (s : ∀ x, E x) (x₀ : B) :
 variable (E)
 
 #print Bundle.contMDiff_proj /-
-theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
+theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π F E) :=
   by
   intro x
   rw [ContMDiffAt, contMDiffWithinAt_iff']
@@ -229,7 +230,7 @@ theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
   apply cont_diff_within_at_fst.congr
   · rintro ⟨a, b⟩ hab
     simp only [mfld_simps] at hab 
-    have : ((chart_at HB x.1).symm (IB.symm a), b) ∈ (trivialization_at F E x.fst).target := by
+    have : ((chart_at HB x.1).symm (IB.symm a), b) ∈ (trivialization_at F E x.proj).target := by
       simp only [hab, mfld_simps]
     simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
   · simp only [mfld_simps]
@@ -237,45 +238,46 @@ theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
 -/
 
 #print Bundle.smooth_proj /-
-theorem smooth_proj : Smooth (IB.Prod 𝓘(𝕜, F)) IB (π E) :=
+theorem smooth_proj : Smooth (IB.Prod 𝓘(𝕜, F)) IB (π F E) :=
   contMDiff_proj E
 #align bundle.smooth_proj Bundle.smooth_proj
 -/
 
 #print Bundle.contMDiffOn_proj /-
-theorem contMDiffOn_proj {s : Set (TotalSpace E)} : ContMDiffOn (IB.Prod 𝓘(𝕜, F)) IB n (π E) s :=
+theorem contMDiffOn_proj {s : Set (TotalSpace F E)} :
+    ContMDiffOn (IB.Prod 𝓘(𝕜, F)) IB n (π F E) s :=
   (Bundle.contMDiff_proj E).ContMDiffOn
 #align bundle.cont_mdiff_on_proj Bundle.contMDiffOn_proj
 -/
 
 #print Bundle.smoothOn_proj /-
-theorem smoothOn_proj {s : Set (TotalSpace E)} : SmoothOn (IB.Prod 𝓘(𝕜, F)) IB (π E) s :=
+theorem smoothOn_proj {s : Set (TotalSpace F E)} : SmoothOn (IB.Prod 𝓘(𝕜, F)) IB (π F E) s :=
   contMDiffOn_proj E
 #align bundle.smooth_on_proj Bundle.smoothOn_proj
 -/
 
 #print Bundle.contMDiffAt_proj /-
-theorem contMDiffAt_proj {p : TotalSpace E} : ContMDiffAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) p :=
+theorem contMDiffAt_proj {p : TotalSpace F E} : ContMDiffAt (IB.Prod 𝓘(𝕜, F)) IB n (π F E) p :=
   (Bundle.contMDiff_proj E).ContMDiffAt
 #align bundle.cont_mdiff_at_proj Bundle.contMDiffAt_proj
 -/
 
 #print Bundle.smoothAt_proj /-
-theorem smoothAt_proj {p : TotalSpace E} : SmoothAt (IB.Prod 𝓘(𝕜, F)) IB (π E) p :=
+theorem smoothAt_proj {p : TotalSpace F E} : SmoothAt (IB.Prod 𝓘(𝕜, F)) IB (π F E) p :=
   Bundle.contMDiffAt_proj E
 #align bundle.smooth_at_proj Bundle.smoothAt_proj
 -/
 
 #print Bundle.contMDiffWithinAt_proj /-
-theorem contMDiffWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
-    ContMDiffWithinAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) s p :=
+theorem contMDiffWithinAt_proj {s : Set (TotalSpace F E)} {p : TotalSpace F E} :
+    ContMDiffWithinAt (IB.Prod 𝓘(𝕜, F)) IB n (π F E) s p :=
   (Bundle.contMDiffAt_proj E).ContMDiffWithinAt
 #align bundle.cont_mdiff_within_at_proj Bundle.contMDiffWithinAt_proj
 -/
 
 #print Bundle.smoothWithinAt_proj /-
-theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
-    SmoothWithinAt (IB.Prod 𝓘(𝕜, F)) IB (π E) s p :=
+theorem smoothWithinAt_proj {s : Set (TotalSpace F E)} {p : TotalSpace F E} :
+    SmoothWithinAt (IB.Prod 𝓘(𝕜, F)) IB (π F E) s p :=
   Bundle.contMDiffWithinAt_proj E
 #align bundle.smooth_within_at_proj Bundle.smoothWithinAt_proj
 -/
@@ -283,7 +285,7 @@ theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
 variable (𝕜 E) [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [VectorBundle 𝕜 F E]
 
 #print Bundle.smooth_zeroSection /-
-theorem smooth_zeroSection : Smooth IB (IB.Prod 𝓘(𝕜, F)) (zeroSection E) :=
+theorem smooth_zeroSection : Smooth IB (IB.Prod 𝓘(𝕜, F)) (zeroSection F E) :=
   by
   intro x
   rw [Bundle.contMDiffAt_totalSpace]
@@ -313,7 +315,7 @@ variable [NontriviallyNormedField 𝕜] {EB : Type _} [NormedAddCommGroup EB] [N
 
 section WithTopology
 
-variable [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
+variable [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)]
 
 variable (F E) [FiberBundle F E] [VectorBundle 𝕜 F E]
 
@@ -324,7 +326,7 @@ registers that the bundle is smooth, in the sense of having smooth transition fu
 This is a mixin, not carrying any new data`. -/
 class SmoothVectorBundle : Prop where
   smoothOn_coordChangeL :
-    ∀ (e e' : Trivialization F (π E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e'],
+    ∀ (e e' : Trivialization F (π F E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e'],
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
         (e.baseSet ∩ e'.baseSet)
 #align smooth_vector_bundle SmoothVectorBundle
@@ -337,7 +339,7 @@ variable [SmoothVectorBundle F E IB]
 /-- For a smooth vector bundle `E` over `B` with fiber modelled on `F`, the change-of-co-ordinates
 between two trivializations `e`, `e'` for `E`, considered as charts to `B × F`, is smooth and
 fiberwise linear. -/
-instance : HasGroupoid (TotalSpace E) (smoothFiberwiseLinear B F IB)
+instance : HasGroupoid (TotalSpace F E) (smoothFiberwiseLinear B F IB)
     where compatible := by
     rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩
     haveI : MemTrivializationAtlas e := ⟨he⟩
@@ -361,7 +363,7 @@ instance : HasGroupoid (TotalSpace E) (smoothFiberwiseLinear B F IB)
       exact e.apply_symm_apply_eq_coord_changeL e' hb' v
 
 /-- A smooth vector bundle `E` is naturally a smooth manifold. -/
-instance : SmoothManifoldWithCorners (IB.Prod 𝓘(𝕜, F)) (TotalSpace E) :=
+instance : SmoothManifoldWithCorners (IB.Prod 𝓘(𝕜, F)) (TotalSpace F E) :=
   by
   refine' { StructureGroupoid.HasGroupoid.comp (smoothFiberwiseLinear B F IB) _ with }
   intro e he
@@ -432,10 +434,10 @@ instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivia
 section Prod
 
 variable (F₁ : Type _) [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _)
-  [TopologicalSpace (TotalSpace E₁)] [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
+  [TopologicalSpace (TotalSpace F₁ E₁)] [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
 
 variable (F₂ : Type _) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type _)
-  [TopologicalSpace (TotalSpace E₂)] [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)]
+  [TopologicalSpace (TotalSpace F₂ E₂)] [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)]
 
 variable [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)] [FiberBundle F₁ E₁]
   [FiberBundle F₂ E₂] [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] [SmoothVectorBundle F₁ E₁ IB]
@@ -479,12 +481,11 @@ class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
     ∀ (e) (_ : e ∈ a.pretrivializationAtlas) (e') (_ : e' ∈ a.pretrivializationAtlas),
       ∃ f : B → F →L[𝕜] F,
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) f (e.baseSet ∩ e'.baseSet) ∧
-          ∀ (b : B) (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F),
-            f b v = (e' (totalSpaceMk b (e.symm b v))).2
+          ∀ (b : B) (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F), f b v = (e' ⟨b, e.symm b v⟩).2
 #align vector_prebundle.is_smooth VectorPrebundle.IsSmooth
 -/
 
-variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π E)}
+variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π F E)}
 
 #print VectorPrebundle.smoothCoordChange /-
 /-- A randomly chosen coordinate change on a `smooth_vector_prebundle`, given by
@@ -509,7 +510,7 @@ theorem smoothOn_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
 #print VectorPrebundle.smoothCoordChange_apply /-
 theorem smoothCoordChange_apply (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
-    a.smoothCoordChange IB he he' b v = (e' (totalSpaceMk b (e.symm b v))).2 :=
+    a.smoothCoordChange IB he he' b v = (e' ⟨b, e.symm b v⟩).2 :=
   (Classical.choose_spec (ha.exists_smooth_coord_change e he e' he')).2 b hb v
 #align vector_prebundle.smooth_coord_change_apply VectorPrebundle.smoothCoordChange_apply
 -/
@@ -517,7 +518,7 @@ theorem smoothCoordChange_apply (he : e ∈ a.pretrivializationAtlas)
 #print VectorPrebundle.mk_smoothCoordChange /-
 theorem mk_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
-    (b, a.smoothCoordChange IB he he' b v) = e' (totalSpaceMk b (e.symm b v)) :=
+    (b, a.smoothCoordChange IB he he' b v) = e' ⟨b, e.symm b v⟩ :=
   by
   ext
   · rw [e.mk_symm hb.1 v, e'.coe_fst', e.proj_symm_apply' hb.1]

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.basic
-! leanprover-community/mathlib commit f9ec187127cc5b381dfcf5f4a22dacca4c20b63d
+! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.VectorBundle.Constructions
 
 /-! # Smooth vector bundles
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines smooth vector bundles over a smooth manifold.
 
 Let `E` be a topological vector bundle, with model fiber `F` and base space `B`.  We consider `E` as

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

@@ -320,14 +320,14 @@ topological vector bundle over `B` with fibers isomorphic to `F`, then `smooth_v
 registers that the bundle is smooth, in the sense of having smooth transition functions.
 This is a mixin, not carrying any new data`. -/
 class SmoothVectorBundle : Prop where
-  smoothOn_coord_change :
+  smoothOn_coordChangeL :
     ∀ (e e' : Trivialization F (π E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e'],
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
         (e.baseSet ∩ e'.baseSet)
 #align smooth_vector_bundle SmoothVectorBundle
 -/
 
-export SmoothVectorBundle (smoothOn_coord_change)
+export SmoothVectorBundle (smoothOn_coordChangeL)
 
 variable [SmoothVectorBundle F E IB]
 
@@ -381,10 +381,10 @@ namespace VectorBundleCore
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
 #print VectorBundleCore.IsSmooth /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coordChangeL] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
-  smoothOn_coord_change :
+  smoothOn_coordChangeL :
     ∀ i j, SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (Z.coordChange i j) (Z.baseSet i ∩ Z.baseSet j)
 #align vector_bundle_core.is_smooth VectorBundleCore.IsSmooth
 -/
@@ -398,7 +398,7 @@ variable [Z.IsSmooth IB]
 /-- If a `vector_bundle_core` has the `is_smooth` mixin, then the vector bundle constructed from it
 is a smooth vector bundle. -/
 instance smoothVectorBundle : SmoothVectorBundle F Z.Fiber IB
-    where smoothOn_coord_change := by
+    where smoothOn_coordChangeL := by
     rintro - - ⟨i, rfl⟩ ⟨i', rfl⟩
     refine' (Z.smooth_on_coord_change IB i i').congr fun b hb => _
     ext v
@@ -414,7 +414,7 @@ end VectorBundleCore
 #print Bundle.Trivial.smoothVectorBundle /-
 /-- A trivial vector bundle over a smooth manifold is a smooth vector bundle. -/
 instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivial B F) IB
-    where smoothOn_coord_change := by
+    where smoothOn_coordChangeL := by
     intro e e' he he'
     obtain rfl := Bundle.Trivial.eq_trivialization B F e
     obtain rfl := Bundle.Trivial.eq_trivialization B F e'
@@ -441,7 +441,7 @@ variable [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E
 #print Bundle.Prod.smoothVectorBundle /-
 /-- The direct sum of two smooth vector bundles over the same base is a smooth vector bundle. -/
 instance Bundle.Prod.smoothVectorBundle : SmoothVectorBundle (F₁ × F₂) (E₁ ×ᵇ E₂) IB
-    where smoothOn_coord_change :=
+    where smoothOn_coordChangeL :=
     by
     rintro _ _ ⟨e₁, e₂, i₁, i₂, rfl⟩ ⟨e₁', e₂', i₁', i₂', rfl⟩
     skip
@@ -531,7 +531,7 @@ theorem smoothVectorBundle :
     @SmoothVectorBundle _ _ F E _ _ _ _ _ _ IB _ _ _ _ _ _ _ a.totalSpaceTopology _ a.toFiberBundle
       a.toVectorBundle :=
   {
-    smoothOn_coord_change := by
+    smoothOn_coordChangeL := by
       rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩
       refine' (a.smooth_on_smooth_coord_change he he').congr _
       intro b hb

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

@@ -82,39 +82,46 @@ section
 variable [TopologicalSpace F] [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
   {HB : Type _} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
+#print FiberBundle.chartedSpace' /-
 /-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
 `B × F`. -/
-instance FiberBundle.chartedSpace : ChartedSpace (B × F) (TotalSpace E)
+instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace E)
     where
   atlas := (fun e : Trivialization F (π E) => e.toLocalHomeomorph) '' trivializationAtlas F E
   chartAt x := (trivializationAt F E x.proj).toLocalHomeomorph
   mem_chart_source x :=
     (trivializationAt F E x.proj).mem_source.mpr (mem_baseSet_trivializationAt F E x.proj)
   chart_mem_atlas x := mem_image_of_mem _ (trivialization_mem_atlas F E _)
-#align fiber_bundle.charted_space FiberBundle.chartedSpace
+#align fiber_bundle.charted_space FiberBundle.chartedSpace'
+-/
 
 section
 
 attribute [local reducible] ModelProd
 
+#print FiberBundle.chartedSpace /-
 /-- Let `B` be a charted space modelled on `HB`.  Then a fiber bundle `E` over a base `B` with model
 fiber `F` is naturally a charted space modelled on `HB.prod F`. -/
-instance FiberBundle.chartedSpace' : ChartedSpace (ModelProd HB F) (TotalSpace E) :=
+instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace E) :=
   ChartedSpace.comp _ (ModelProd B F) _
-#align fiber_bundle.charted_space' FiberBundle.chartedSpace'
+#align fiber_bundle.charted_space' FiberBundle.chartedSpace
+-/
 
 end
 
+#print FiberBundle.chartedSpace_chartAt /-
 theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
     chartAt (ModelProd HB F) x =
       (trivializationAt F E x.proj).toLocalHomeomorph ≫ₕ
         (chartAt HB x.proj).Prod (LocalHomeomorph.refl F) :=
   by
-  dsimp only [FiberBundle.chartedSpace', ChartedSpace.comp, FiberBundle.chartedSpace,
+  dsimp only [FiberBundle.chartedSpace, ChartedSpace.comp, FiberBundle.chartedSpace',
     prodChartedSpace, chartedSpaceSelf]
   rw [Trivialization.coe_coe, Trivialization.coe_fst' _ (mem_base_set_trivialization_at F E x.proj)]
 #align fiber_bundle.charted_space_chart_at FiberBundle.chartedSpace_chartAt
+-/
 
+#print FiberBundle.chartedSpace_chartAt_symm_fst /-
 theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace E) (y : ModelProd HB F)
     (hy : y ∈ (chartAt (ModelProd HB F) x).target) :
     ((chartAt (ModelProd HB F) x).symm y).proj = (chartAt HB x.proj).symm y.1 :=
@@ -122,6 +129,7 @@ theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace E) (y : ModelP
   simp only [FiberBundle.chartedSpace_chartAt, mfld_simps] at hy ⊢
   exact (trivialization_at F E x.proj).proj_symm_apply hy.2
 #align fiber_bundle.charted_space_chart_at_symm_fst FiberBundle.chartedSpace_chartAt_symm_fst
+-/
 
 end
 
@@ -137,6 +145,7 @@ variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜
 
 variable [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
+#print FiberBundle.extChartAt /-
 protected theorem FiberBundle.extChartAt (x : TotalSpace E) :
     extChartAt (IB.Prod 𝓘(𝕜, F)) x =
       (trivializationAt F E x.proj).toLocalEquiv ≫
@@ -145,6 +154,7 @@ protected theorem FiberBundle.extChartAt (x : TotalSpace E) :
   simp_rw [extChartAt, FiberBundle.chartedSpace_chartAt, extend]
   simp only [LocalEquiv.trans_assoc, mfld_simps]
 #align fiber_bundle.ext_chart_at FiberBundle.extChartAt
+-/
 
 /-! ### Smoothness of maps in/out fiber bundles
 
@@ -157,6 +167,7 @@ namespace Bundle
 
 variable {F E IB}
 
+#print Bundle.contMDiffWithinAt_totalSpace /-
 /-- Characterization of C^n functions into a smooth vector bundle. -/
 theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀ : M} :
     ContMDiffWithinAt IM (IB.Prod 𝓘(𝕜, F)) n f s x₀ ↔
@@ -182,7 +193,9 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀
     exact hx
   · simp only [mfld_simps]
 #align bundle.cont_mdiff_within_at_total_space Bundle.contMDiffWithinAt_totalSpace
+-/
 
+#print Bundle.contMDiffAt_totalSpace /-
 /-- Characterization of C^n functions into a smooth vector bundle. -/
 theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
     ContMDiffAt IM (IB.Prod 𝓘(𝕜, F)) n f x₀ ↔
@@ -190,16 +203,20 @@ theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
         ContMDiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ :=
   by simp_rw [← contMDiffWithinAt_univ]; exact cont_mdiff_within_at_total_space f
 #align bundle.cont_mdiff_at_total_space Bundle.contMDiffAt_totalSpace
+-/
 
+#print Bundle.contMDiffAt_section /-
 /-- Characterization of C^n sections of a smooth vector bundle. -/
 theorem contMDiffAt_section (s : ∀ x, E x) (x₀ : B) :
     ContMDiffAt IB (IB.Prod 𝓘(𝕜, F)) n (fun x => totalSpaceMk x (s x)) x₀ ↔
       ContMDiffAt IB 𝓘(𝕜, F) n (fun x => (trivializationAt F E x₀ (totalSpaceMk x (s x))).2) x₀ :=
   by simp_rw [cont_mdiff_at_total_space, and_iff_right_iff_imp]; intro x; exact contMDiffAt_id
 #align bundle.cont_mdiff_at_section Bundle.contMDiffAt_section
+-/
 
 variable (E)
 
+#print Bundle.contMDiff_proj /-
 theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
   by
   intro x
@@ -214,39 +231,55 @@ theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
     simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
   · simp only [mfld_simps]
 #align bundle.cont_mdiff_proj Bundle.contMDiff_proj
+-/
 
+#print Bundle.smooth_proj /-
 theorem smooth_proj : Smooth (IB.Prod 𝓘(𝕜, F)) IB (π E) :=
   contMDiff_proj E
 #align bundle.smooth_proj Bundle.smooth_proj
+-/
 
+#print Bundle.contMDiffOn_proj /-
 theorem contMDiffOn_proj {s : Set (TotalSpace E)} : ContMDiffOn (IB.Prod 𝓘(𝕜, F)) IB n (π E) s :=
   (Bundle.contMDiff_proj E).ContMDiffOn
 #align bundle.cont_mdiff_on_proj Bundle.contMDiffOn_proj
+-/
 
+#print Bundle.smoothOn_proj /-
 theorem smoothOn_proj {s : Set (TotalSpace E)} : SmoothOn (IB.Prod 𝓘(𝕜, F)) IB (π E) s :=
   contMDiffOn_proj E
 #align bundle.smooth_on_proj Bundle.smoothOn_proj
+-/
 
+#print Bundle.contMDiffAt_proj /-
 theorem contMDiffAt_proj {p : TotalSpace E} : ContMDiffAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) p :=
   (Bundle.contMDiff_proj E).ContMDiffAt
 #align bundle.cont_mdiff_at_proj Bundle.contMDiffAt_proj
+-/
 
+#print Bundle.smoothAt_proj /-
 theorem smoothAt_proj {p : TotalSpace E} : SmoothAt (IB.Prod 𝓘(𝕜, F)) IB (π E) p :=
   Bundle.contMDiffAt_proj E
 #align bundle.smooth_at_proj Bundle.smoothAt_proj
+-/
 
+#print Bundle.contMDiffWithinAt_proj /-
 theorem contMDiffWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
     ContMDiffWithinAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) s p :=
   (Bundle.contMDiffAt_proj E).ContMDiffWithinAt
 #align bundle.cont_mdiff_within_at_proj Bundle.contMDiffWithinAt_proj
+-/
 
+#print Bundle.smoothWithinAt_proj /-
 theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
     SmoothWithinAt (IB.Prod 𝓘(𝕜, F)) IB (π E) s p :=
   Bundle.contMDiffWithinAt_proj E
 #align bundle.smooth_within_at_proj Bundle.smoothWithinAt_proj
+-/
 
 variable (𝕜 E) [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [VectorBundle 𝕜 F E]
 
+#print Bundle.smooth_zeroSection /-
 theorem smooth_zeroSection : Smooth IB (IB.Prod 𝓘(𝕜, F)) (zeroSection E) :=
   by
   intro x
@@ -259,6 +292,7 @@ theorem smooth_zeroSection : Smooth IB (IB.Prod 𝓘(𝕜, F)) (zeroSection E) :
       fun x' hx' => _
   simp_rw [zero_section_proj, (trivialization_at F E x).zeroSection 𝕜 hx']
 #align bundle.smooth_zero_section Bundle.smooth_zeroSection
+-/
 
 end Bundle
 
@@ -280,6 +314,7 @@ variable [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
 
 variable (F E) [FiberBundle F E] [VectorBundle 𝕜 F E]
 
+#print SmoothVectorBundle /-
 /-- When `B` is a smooth manifold with corners with respect to a model `IB` and `E` is a
 topological vector bundle over `B` with fibers isomorphic to `F`, then `smooth_vector_bundle F E IB`
 registers that the bundle is smooth, in the sense of having smooth transition functions.
@@ -290,6 +325,7 @@ class SmoothVectorBundle : Prop where
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
         (e.baseSet ∩ e'.baseSet)
 #align smooth_vector_bundle SmoothVectorBundle
+-/
 
 export SmoothVectorBundle (smoothOn_coord_change)
 
@@ -344,18 +380,21 @@ namespace VectorBundleCore
 
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
+#print VectorBundleCore.IsSmooth /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coord_change :
     ∀ i j, SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (Z.coordChange i j) (Z.baseSet i ∩ Z.baseSet j)
 #align vector_bundle_core.is_smooth VectorBundleCore.IsSmooth
+-/
 
 /- ./././Mathport/Syntax/Translate/Command.lean:240:13: unsupported: advanced export style -/
 export IsSmooth ()
 
 variable [Z.IsSmooth IB]
 
+#print VectorBundleCore.smoothVectorBundle /-
 /-- If a `vector_bundle_core` has the `is_smooth` mixin, then the vector bundle constructed from it
 is a smooth vector bundle. -/
 instance smoothVectorBundle : SmoothVectorBundle F Z.Fiber IB
@@ -365,12 +404,14 @@ instance smoothVectorBundle : SmoothVectorBundle F Z.Fiber IB
     ext v
     exact Z.local_triv_coord_change_eq i i' hb v
 #align vector_bundle_core.smooth_vector_bundle VectorBundleCore.smoothVectorBundle
+-/
 
 end VectorBundleCore
 
 /-! ### The trivial smooth vector bundle -/
 
 
+#print Bundle.Trivial.smoothVectorBundle /-
 /-- A trivial vector bundle over a smooth manifold is a smooth vector bundle. -/
 instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivial B F) IB
     where smoothOn_coord_change := by
@@ -380,6 +421,7 @@ instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivia
     simp_rw [Bundle.Trivial.trivialization.coordChangeL]
     exact smooth_const.smooth_on
 #align bundle.trivial.smooth_vector_bundle Bundle.Trivial.smoothVectorBundle
+-/
 
 /-! ### Direct sums of smooth vector bundles -/
 
@@ -396,6 +438,7 @@ variable [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E
   [FiberBundle F₂ E₂] [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] [SmoothVectorBundle F₁ E₁ IB]
   [SmoothVectorBundle F₂ E₂ IB]
 
+#print Bundle.Prod.smoothVectorBundle /-
 /-- The direct sum of two smooth vector bundles over the same base is a smooth vector bundle. -/
 instance Bundle.Prod.smoothVectorBundle : SmoothVectorBundle (F₁ × F₂) (E₁ ×ᵇ E₂) IB
     where smoothOn_coord_change :=
@@ -412,6 +455,7 @@ instance Bundle.Prod.smoothVectorBundle : SmoothVectorBundle (F₁ × F₂) (E
       simp only [Trivialization.baseSet_prod, mfld_simps]
       mfld_set_tac
 #align bundle.prod.smooth_vector_bundle Bundle.Prod.smoothVectorBundle
+-/
 
 end Prod
 
@@ -424,6 +468,7 @@ namespace VectorPrebundle
 
 variable [∀ x, TopologicalSpace (E x)] {F E}
 
+#print VectorPrebundle.IsSmooth /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
 /-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
 class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
@@ -434,9 +479,11 @@ class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
           ∀ (b : B) (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F),
             f b v = (e' (totalSpaceMk b (e.symm b v))).2
 #align vector_prebundle.is_smooth VectorPrebundle.IsSmooth
+-/
 
 variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π E)}
 
+#print VectorPrebundle.smoothCoordChange /-
 /-- A randomly chosen coordinate change on a `smooth_vector_prebundle`, given by
   the field `exists_coord_change`. Note that `a.smooth_coord_change` need not be the same as
   `a.coord_change`. -/
@@ -444,21 +491,27 @@ noncomputable def smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) (b : B) : F →L[𝕜] F :=
   Classical.choose (ha.exists_smooth_coord_change e he e' he') b
 #align vector_prebundle.smooth_coord_change VectorPrebundle.smoothCoordChange
+-/
 
 variable {IB}
 
+#print VectorPrebundle.smoothOn_smoothCoordChange /-
 theorem smoothOn_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) :
     SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (a.smoothCoordChange IB he he') (e.baseSet ∩ e'.baseSet) :=
   (Classical.choose_spec (ha.exists_smooth_coord_change e he e' he')).1
 #align vector_prebundle.smooth_on_smooth_coord_change VectorPrebundle.smoothOn_smoothCoordChange
+-/
 
+#print VectorPrebundle.smoothCoordChange_apply /-
 theorem smoothCoordChange_apply (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
     a.smoothCoordChange IB he he' b v = (e' (totalSpaceMk b (e.symm b v))).2 :=
   (Classical.choose_spec (ha.exists_smooth_coord_change e he e' he')).2 b hb v
 #align vector_prebundle.smooth_coord_change_apply VectorPrebundle.smoothCoordChange_apply
+-/
 
+#print VectorPrebundle.mk_smoothCoordChange /-
 theorem mk_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
     (b, a.smoothCoordChange IB he he' b v) = e' (totalSpaceMk b (e.symm b v)) :=
@@ -468,13 +521,15 @@ theorem mk_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
     rw [e.proj_symm_apply' hb.1]; exact hb.2
   · exact a.smooth_coord_change_apply he he' hb v
 #align vector_prebundle.mk_smooth_coord_change VectorPrebundle.mk_smoothCoordChange
+-/
 
 variable (IB)
 
+#print VectorPrebundle.smoothVectorBundle /-
 /-- Make a `smooth_vector_bundle` from a `smooth_vector_prebundle`.  -/
 theorem smoothVectorBundle :
     @SmoothVectorBundle _ _ F E _ _ _ _ _ _ IB _ _ _ _ _ _ _ a.totalSpaceTopology _ a.toFiberBundle
-      a.to_vectorBundle :=
+      a.toVectorBundle :=
   {
     smoothOn_coord_change := by
       rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩
@@ -485,6 +540,7 @@ theorem smoothVectorBundle :
         Trivialization.coordChangeL_apply]
       exacts [rfl, hb] }
 #align vector_prebundle.smooth_vector_bundle VectorPrebundle.smoothVectorBundle
+-/
 
 end VectorPrebundle
 

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

@@ -158,18 +158,18 @@ namespace Bundle
 variable {F E IB}
 
 /-- Characterization of C^n functions into a smooth vector bundle. -/
-theorem contMdiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀ : M} :
-    ContMdiffWithinAt IM (IB.Prod 𝓘(𝕜, F)) n f s x₀ ↔
-      ContMdiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
-        ContMdiffWithinAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) s x₀ :=
+theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀ : M} :
+    ContMDiffWithinAt IM (IB.Prod 𝓘(𝕜, F)) n f s x₀ ↔
+      ContMDiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
+        ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) s x₀ :=
   by
-  simp (config := { singlePass := true }) only [contMdiffWithinAt_iff_target]
+  simp (config := { singlePass := true }) only [contMDiffWithinAt_iff_target]
   rw [and_and_and_comm, ← continuous_within_at_total_space, and_congr_right_iff]
   intro hf
   simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp, LocalEquiv.trans_apply,
     LocalEquiv.prod_coe, LocalEquiv.refl_coe, extChartAt_self_apply, modelWithCornersSelf_coe,
     id_def]
-  refine' (contMdiffWithinAt_prod_iff _).trans _
+  refine' (contMDiffWithinAt_prod_iff _).trans _
   -- rw doesn't do this?
   have h1 : (fun x => (f x).proj) ⁻¹' (trivialization_at F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
     ((continuous_proj F E).ContinuousWithinAt.comp hf (maps_to_image f s)).preimage_mem_nhdsWithin
@@ -181,29 +181,29 @@ theorem contMdiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀
     rw [Trivialization.coe_fst']
     exact hx
   · simp only [mfld_simps]
-#align bundle.cont_mdiff_within_at_total_space Bundle.contMdiffWithinAt_totalSpace
+#align bundle.cont_mdiff_within_at_total_space Bundle.contMDiffWithinAt_totalSpace
 
 /-- Characterization of C^n functions into a smooth vector bundle. -/
-theorem contMdiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
-    ContMdiffAt IM (IB.Prod 𝓘(𝕜, F)) n f x₀ ↔
-      ContMdiffAt IM IB n (fun x => (f x).proj) x₀ ∧
-        ContMdiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ :=
-  by simp_rw [← contMdiffWithinAt_univ]; exact cont_mdiff_within_at_total_space f
-#align bundle.cont_mdiff_at_total_space Bundle.contMdiffAt_totalSpace
+theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
+    ContMDiffAt IM (IB.Prod 𝓘(𝕜, F)) n f x₀ ↔
+      ContMDiffAt IM IB n (fun x => (f x).proj) x₀ ∧
+        ContMDiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ :=
+  by simp_rw [← contMDiffWithinAt_univ]; exact cont_mdiff_within_at_total_space f
+#align bundle.cont_mdiff_at_total_space Bundle.contMDiffAt_totalSpace
 
 /-- Characterization of C^n sections of a smooth vector bundle. -/
-theorem contMdiffAt_section (s : ∀ x, E x) (x₀ : B) :
-    ContMdiffAt IB (IB.Prod 𝓘(𝕜, F)) n (fun x => totalSpaceMk x (s x)) x₀ ↔
-      ContMdiffAt IB 𝓘(𝕜, F) n (fun x => (trivializationAt F E x₀ (totalSpaceMk x (s x))).2) x₀ :=
-  by simp_rw [cont_mdiff_at_total_space, and_iff_right_iff_imp]; intro x; exact contMdiffAt_id
-#align bundle.cont_mdiff_at_section Bundle.contMdiffAt_section
+theorem contMDiffAt_section (s : ∀ x, E x) (x₀ : B) :
+    ContMDiffAt IB (IB.Prod 𝓘(𝕜, F)) n (fun x => totalSpaceMk x (s x)) x₀ ↔
+      ContMDiffAt IB 𝓘(𝕜, F) n (fun x => (trivializationAt F E x₀ (totalSpaceMk x (s x))).2) x₀ :=
+  by simp_rw [cont_mdiff_at_total_space, and_iff_right_iff_imp]; intro x; exact contMDiffAt_id
+#align bundle.cont_mdiff_at_section Bundle.contMDiffAt_section
 
 variable (E)
 
-theorem contMdiff_proj : ContMdiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
+theorem contMDiff_proj : ContMDiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
   by
   intro x
-  rw [ContMdiffAt, contMdiffWithinAt_iff']
+  rw [ContMDiffAt, contMDiffWithinAt_iff']
   refine' ⟨(continuous_proj F E).ContinuousWithinAt, _⟩
   simp_rw [(· ∘ ·), FiberBundle.extChartAt]
   apply cont_diff_within_at_fst.congr
@@ -213,36 +213,36 @@ theorem contMdiff_proj : ContMdiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
       simp only [hab, mfld_simps]
     simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
   · simp only [mfld_simps]
-#align bundle.cont_mdiff_proj Bundle.contMdiff_proj
+#align bundle.cont_mdiff_proj Bundle.contMDiff_proj
 
 theorem smooth_proj : Smooth (IB.Prod 𝓘(𝕜, F)) IB (π E) :=
-  contMdiff_proj E
+  contMDiff_proj E
 #align bundle.smooth_proj Bundle.smooth_proj
 
-theorem contMdiffOn_proj {s : Set (TotalSpace E)} : ContMdiffOn (IB.Prod 𝓘(𝕜, F)) IB n (π E) s :=
-  (Bundle.contMdiff_proj E).ContMdiffOn
-#align bundle.cont_mdiff_on_proj Bundle.contMdiffOn_proj
+theorem contMDiffOn_proj {s : Set (TotalSpace E)} : ContMDiffOn (IB.Prod 𝓘(𝕜, F)) IB n (π E) s :=
+  (Bundle.contMDiff_proj E).ContMDiffOn
+#align bundle.cont_mdiff_on_proj Bundle.contMDiffOn_proj
 
 theorem smoothOn_proj {s : Set (TotalSpace E)} : SmoothOn (IB.Prod 𝓘(𝕜, F)) IB (π E) s :=
-  contMdiffOn_proj E
+  contMDiffOn_proj E
 #align bundle.smooth_on_proj Bundle.smoothOn_proj
 
-theorem contMdiffAt_proj {p : TotalSpace E} : ContMdiffAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) p :=
-  (Bundle.contMdiff_proj E).ContMdiffAt
-#align bundle.cont_mdiff_at_proj Bundle.contMdiffAt_proj
+theorem contMDiffAt_proj {p : TotalSpace E} : ContMDiffAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) p :=
+  (Bundle.contMDiff_proj E).ContMDiffAt
+#align bundle.cont_mdiff_at_proj Bundle.contMDiffAt_proj
 
 theorem smoothAt_proj {p : TotalSpace E} : SmoothAt (IB.Prod 𝓘(𝕜, F)) IB (π E) p :=
-  Bundle.contMdiffAt_proj E
+  Bundle.contMDiffAt_proj E
 #align bundle.smooth_at_proj Bundle.smoothAt_proj
 
-theorem contMdiffWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
-    ContMdiffWithinAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) s p :=
-  (Bundle.contMdiffAt_proj E).ContMdiffWithinAt
-#align bundle.cont_mdiff_within_at_proj Bundle.contMdiffWithinAt_proj
+theorem contMDiffWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
+    ContMDiffWithinAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) s p :=
+  (Bundle.contMDiffAt_proj E).ContMDiffWithinAt
+#align bundle.cont_mdiff_within_at_proj Bundle.contMDiffWithinAt_proj
 
 theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
     SmoothWithinAt (IB.Prod 𝓘(𝕜, F)) IB (π E) s p :=
-  Bundle.contMdiffWithinAt_proj E
+  Bundle.contMDiffWithinAt_proj E
 #align bundle.smooth_within_at_proj Bundle.smoothWithinAt_proj
 
 variable (𝕜 E) [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [VectorBundle 𝕜 F E]
@@ -250,8 +250,8 @@ variable (𝕜 E) [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [Vecto
 theorem smooth_zeroSection : Smooth IB (IB.Prod 𝓘(𝕜, F)) (zeroSection E) :=
   by
   intro x
-  rw [Bundle.contMdiffAt_totalSpace]
-  refine' ⟨contMdiffAt_id, cont_mdiff_at_const.congr_of_eventually_eq _⟩
+  rw [Bundle.contMDiffAt_totalSpace]
+  refine' ⟨contMDiffAt_id, cont_mdiff_at_const.congr_of_eventually_eq _⟩
   · exact 0
   refine'
     eventually_of_mem
@@ -307,7 +307,7 @@ instance : HasGroupoid (TotalSpace E) (smoothFiberwiseLinear B F IB)
     rw [mem_smoothFiberwiseLinear_iff]
     refine' ⟨_, _, e.open_base_set.inter e'.open_base_set, smooth_on_coord_change e e', _, _, _⟩
     · rw [inter_comm]
-      apply ContMdiffOn.congr (smooth_on_coord_change e' e)
+      apply ContMDiffOn.congr (smooth_on_coord_change e' e)
       · intro b hb
         rw [e.symm_coord_changeL e' hb]
       · infer_instance
@@ -328,14 +328,14 @@ instance : SmoothManifoldWithCorners (IB.Prod 𝓘(𝕜, F)) (TotalSpace E) :=
   intro e he
   rw [mem_smoothFiberwiseLinear_iff] at he 
   obtain ⟨φ, U, hU, hφ, h2φ, heφ⟩ := he
-  rw [is_local_structomorph_on_contDiffGroupoid_iff]
-  refine' ⟨ContMdiffOn.congr _ heφ.eq_on, ContMdiffOn.congr _ heφ.symm'.eq_on⟩
+  rw [isLocalStructomorphOn_contDiffGroupoid_iff]
+  refine' ⟨ContMDiffOn.congr _ heφ.eq_on, ContMDiffOn.congr _ heφ.symm'.eq_on⟩
   · rw [heφ.source_eq]
     apply smooth_on_fst.prod_mk
-    exact (hφ.comp contMdiffOn_fst <| prod_subset_preimage_fst _ _).clm_apply contMdiffOn_snd
+    exact (hφ.comp contMDiffOn_fst <| prod_subset_preimage_fst _ _).clm_apply contMDiffOn_snd
   · rw [heφ.target_eq]
     apply smooth_on_fst.prod_mk
-    exact (h2φ.comp contMdiffOn_fst <| prod_subset_preimage_fst _ _).clm_apply contMdiffOn_snd
+    exact (h2φ.comp contMDiffOn_fst <| prod_subset_preimage_fst _ _).clm_apply contMDiffOn_snd
 
 /-! ### Core construction for smooth vector bundles -/
 
@@ -403,8 +403,8 @@ instance Bundle.Prod.smoothVectorBundle : SmoothVectorBundle (F₁ × F₂) (E
     rintro _ _ ⟨e₁, e₂, i₁, i₂, rfl⟩ ⟨e₁', e₂', i₁', i₂', rfl⟩
     skip
     rw [SmoothOn]
-    refine' ContMdiffOn.congr _ (e₁.coord_changeL_prod 𝕜 e₁' e₂ e₂')
-    refine' ContMdiffOn.clm_prodMap _ _
+    refine' ContMDiffOn.congr _ (e₁.coord_changeL_prod 𝕜 e₁' e₂ e₂')
+    refine' ContMDiffOn.clm_prodMap _ _
     · refine' (smooth_on_coord_change e₁ e₁').mono _
       simp only [Trivialization.baseSet_prod, mfld_simps]
       mfld_set_tac

mathlib commit https://github.com/leanprover-community/mathlib/commit/9f55d0d4363ae59948c33864cbc52e0b12e0e8ce

@@ -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.basic
-! leanprover-community/mathlib commit f7ebde7ee0d1505dfccac8644ae12371aa3c1c9f
+! leanprover-community/mathlib commit f9ec187127cc5b381dfcf5f4a22dacca4c20b63d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -191,6 +191,13 @@ theorem contMdiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
   by simp_rw [← contMdiffWithinAt_univ]; exact cont_mdiff_within_at_total_space f
 #align bundle.cont_mdiff_at_total_space Bundle.contMdiffAt_totalSpace
 
+/-- Characterization of C^n sections of a smooth vector bundle. -/
+theorem contMdiffAt_section (s : ∀ x, E x) (x₀ : B) :
+    ContMdiffAt IB (IB.Prod 𝓘(𝕜, F)) n (fun x => totalSpaceMk x (s x)) x₀ ↔
+      ContMdiffAt IB 𝓘(𝕜, F) n (fun x => (trivializationAt F E x₀ (totalSpaceMk x (s x))).2) x₀ :=
+  by simp_rw [cont_mdiff_at_total_space, and_iff_right_iff_imp]; intro x; exact contMdiffAt_id
+#align bundle.cont_mdiff_at_section Bundle.contMdiffAt_section
+
 variable (E)
 
 theorem contMdiff_proj : ContMdiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=

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

@@ -337,7 +337,7 @@ namespace VectorBundleCore
 
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coord_change :
@@ -430,8 +430,6 @@ class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
 
 variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π E)}
 
-include ha
-
 /-- A randomly chosen coordinate change on a `smooth_vector_prebundle`, given by
   the field `exists_coord_change`. Note that `a.smooth_coord_change` need not be the same as
   `a.coord_change`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -417,7 +417,7 @@ namespace VectorPrebundle
 
 variable [∀ x, TopologicalSpace (E x)] {F E}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
 /-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
 class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
   exists_smooth_coord_change :

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

@@ -337,14 +337,14 @@ namespace VectorBundleCore
 
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coord_change :
     ∀ i j, SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (Z.coordChange i j) (Z.baseSet i ∩ Z.baseSet j)
 #align vector_bundle_core.is_smooth VectorBundleCore.IsSmooth
 
-/- ./././Mathport/Syntax/Translate/Command.lean:239:13: unsupported: advanced export style -/
+/- ./././Mathport/Syntax/Translate/Command.lean:240:13: unsupported: advanced export style -/
 export IsSmooth ()
 
 variable [Z.IsSmooth IB]

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

@@ -119,7 +119,7 @@ theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace E) (y : ModelP
     (hy : y ∈ (chartAt (ModelProd HB F) x).target) :
     ((chartAt (ModelProd HB F) x).symm y).proj = (chartAt HB x.proj).symm y.1 :=
   by
-  simp only [FiberBundle.chartedSpace_chartAt, mfld_simps] at hy⊢
+  simp only [FiberBundle.chartedSpace_chartAt, mfld_simps] at hy ⊢
   exact (trivialization_at F E x.proj).proj_symm_apply hy.2
 #align fiber_bundle.charted_space_chart_at_symm_fst FiberBundle.chartedSpace_chartAt_symm_fst
 
@@ -201,7 +201,7 @@ theorem contMdiff_proj : ContMdiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
   simp_rw [(· ∘ ·), FiberBundle.extChartAt]
   apply cont_diff_within_at_fst.congr
   · rintro ⟨a, b⟩ hab
-    simp only [mfld_simps] at hab
+    simp only [mfld_simps] at hab 
     have : ((chart_at HB x.1).symm (IB.symm a), b) ∈ (trivialization_at F E x.fst).target := by
       simp only [hab, mfld_simps]
     simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
@@ -319,7 +319,7 @@ instance : SmoothManifoldWithCorners (IB.Prod 𝓘(𝕜, F)) (TotalSpace E) :=
   by
   refine' { StructureGroupoid.HasGroupoid.comp (smoothFiberwiseLinear B F IB) _ with }
   intro e he
-  rw [mem_smoothFiberwiseLinear_iff] at he
+  rw [mem_smoothFiberwiseLinear_iff] at he 
   obtain ⟨φ, U, hU, hφ, h2φ, heφ⟩ := he
   rw [is_local_structomorph_on_contDiffGroupoid_iff]
   refine' ⟨ContMdiffOn.congr _ heφ.eq_on, ContMdiffOn.congr _ heφ.symm'.eq_on⟩
@@ -478,7 +478,7 @@ theorem smoothVectorBundle :
       ext v
       rw [a.smooth_coord_change_apply he he' hb v, ContinuousLinearEquiv.coe_coe,
         Trivialization.coordChangeL_apply]
-      exacts[rfl, hb] }
+      exacts [rfl, hb] }
 #align vector_prebundle.smooth_vector_bundle VectorPrebundle.smoothVectorBundle
 
 end VectorPrebundle

mathlib commit https://github.com/leanprover-community/mathlib/commit/88a563b158f59f2983cfad685664da95502e8cdd

@@ -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.basic
-! leanprover-community/mathlib commit c89fe2d59ae06402c3f55f978016d1ada444f57e
+! leanprover-community/mathlib commit f7ebde7ee0d1505dfccac8644ae12371aa3c1c9f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -415,7 +415,7 @@ end WithTopology
 
 namespace VectorPrebundle
 
-variable {F E}
+variable [∀ x, TopologicalSpace (E x)] {F E}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
 /-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
@@ -468,8 +468,8 @@ variable (IB)
 
 /-- Make a `smooth_vector_bundle` from a `smooth_vector_prebundle`.  -/
 theorem smoothVectorBundle :
-    @SmoothVectorBundle _ _ F E _ _ _ _ _ _ IB _ _ _ _ _ _ _ a.totalSpaceTopology a.fiberTopology
-      a.toFiberBundle a.to_vectorBundle :=
+    @SmoothVectorBundle _ _ F E _ _ _ _ _ _ IB _ _ _ _ _ _ _ a.totalSpaceTopology _ a.toFiberBundle
+      a.to_vectorBundle :=
   {
     smoothOn_coord_change := by
       rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩

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

@@ -70,7 +70,7 @@ open Function (id_def)
 
 open Filter
 
-open Manifold Bundle Topology
+open scoped Manifold Bundle Topology
 
 variable {𝕜 B B' F M : Type _} {E : B → Type _}
 

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

@@ -188,9 +188,7 @@ theorem contMdiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
     ContMdiffAt IM (IB.Prod 𝓘(𝕜, F)) n f x₀ ↔
       ContMdiffAt IM IB n (fun x => (f x).proj) x₀ ∧
         ContMdiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ :=
-  by
-  simp_rw [← contMdiffWithinAt_univ]
-  exact cont_mdiff_within_at_total_space f
+  by simp_rw [← contMdiffWithinAt_univ]; exact cont_mdiff_within_at_total_space f
 #align bundle.cont_mdiff_at_total_space Bundle.contMdiffAt_totalSpace
 
 variable (E)
@@ -462,8 +460,7 @@ theorem mk_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
   by
   ext
   · rw [e.mk_symm hb.1 v, e'.coe_fst', e.proj_symm_apply' hb.1]
-    rw [e.proj_symm_apply' hb.1]
-    exact hb.2
+    rw [e.proj_symm_apply' hb.1]; exact hb.2
   · exact a.smooth_coord_change_apply he he' hb v
 #align vector_prebundle.mk_smooth_coord_change VectorPrebundle.mk_smoothCoordChange
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -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.basic
-! leanprover-community/mathlib commit 0187644979f2d3e10a06e916a869c994facd9a87
+! leanprover-community/mathlib commit c89fe2d59ae06402c3f55f978016d1ada444f57e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -49,9 +49,13 @@ fields, they can also be C^k vector bundles, etc.
 * `bundle.total_space.smooth_manifold_with_corners`: A smooth vector bundle is naturally a smooth
   manifold.
 
-* `vector_bundle_core.smooth_vector_bundle`: If a (topological) `vector_bundle_core` is smooth, in
-  the sense of having smooth transition functions, then the vector bundle constructed from it is a
-  smooth vector bundle.
+* `vector_bundle_core.smooth_vector_bundle`: If a (topological) `vector_bundle_core` is smooth,
+  in the sense of having smooth transition functions (cf. `vector_bundle_core.is_smooth`),
+  then the vector bundle constructed from it is a smooth vector bundle.
+
+* `vector_prebundle.smooth_vector_bundle`: If a `vector_prebundle` is smooth,
+  in the sense of having smooth transition functions (cf. `vector_prebundle.is_smooth`),
+  then the vector bundle constructed from it is a smooth vector bundle.
 
 * `bundle.prod.smooth_vector_bundle`: The direct sum of two smooth vector bundles is a smooth vector
   bundle.
@@ -258,13 +262,16 @@ end
 /-! ### Smooth vector bundles -/
 
 
-variable [NontriviallyNormedField 𝕜] [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)]
-  [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace (TotalSpace E)]
-  [∀ x, TopologicalSpace (E x)] {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB]
+variable [NontriviallyNormedField 𝕜] {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB]
   {HB : Type _} [TopologicalSpace HB] (IB : ModelWithCorners 𝕜 EB HB) [TopologicalSpace B]
   [ChartedSpace HB B] [SmoothManifoldWithCorners IB B] {EM : Type _} [NormedAddCommGroup EM]
   [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
   [TopologicalSpace M] [ChartedSpace HM M] [Is : SmoothManifoldWithCorners IM M] {n : ℕ∞}
+  [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+
+section WithTopology
+
+variable [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
 
 variable (F E) [FiberBundle F E] [VectorBundle 𝕜 F E]
 
@@ -403,3 +410,79 @@ instance Bundle.Prod.smoothVectorBundle : SmoothVectorBundle (F₁ × F₂) (E
 
 end Prod
 
+end WithTopology
+
+/-! ### Prebundle construction for smooth vector bundles -/
+
+
+namespace VectorPrebundle
+
+variable {F E}
+
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » a.pretrivialization_atlas) -/
+/-- Mixin for a `vector_prebundle` stating smoothness of coordinate changes. -/
+class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
+  exists_smooth_coord_change :
+    ∀ (e) (_ : e ∈ a.pretrivializationAtlas) (e') (_ : e' ∈ a.pretrivializationAtlas),
+      ∃ f : B → F →L[𝕜] F,
+        SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) f (e.baseSet ∩ e'.baseSet) ∧
+          ∀ (b : B) (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F),
+            f b v = (e' (totalSpaceMk b (e.symm b v))).2
+#align vector_prebundle.is_smooth VectorPrebundle.IsSmooth
+
+variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π E)}
+
+include ha
+
+/-- A randomly chosen coordinate change on a `smooth_vector_prebundle`, given by
+  the field `exists_coord_change`. Note that `a.smooth_coord_change` need not be the same as
+  `a.coord_change`. -/
+noncomputable def smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
+    (he' : e' ∈ a.pretrivializationAtlas) (b : B) : F →L[𝕜] F :=
+  Classical.choose (ha.exists_smooth_coord_change e he e' he') b
+#align vector_prebundle.smooth_coord_change VectorPrebundle.smoothCoordChange
+
+variable {IB}
+
+theorem smoothOn_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
+    (he' : e' ∈ a.pretrivializationAtlas) :
+    SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (a.smoothCoordChange IB he he') (e.baseSet ∩ e'.baseSet) :=
+  (Classical.choose_spec (ha.exists_smooth_coord_change e he e' he')).1
+#align vector_prebundle.smooth_on_smooth_coord_change VectorPrebundle.smoothOn_smoothCoordChange
+
+theorem smoothCoordChange_apply (he : e ∈ a.pretrivializationAtlas)
+    (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
+    a.smoothCoordChange IB he he' b v = (e' (totalSpaceMk b (e.symm b v))).2 :=
+  (Classical.choose_spec (ha.exists_smooth_coord_change e he e' he')).2 b hb v
+#align vector_prebundle.smooth_coord_change_apply VectorPrebundle.smoothCoordChange_apply
+
+theorem mk_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
+    (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
+    (b, a.smoothCoordChange IB he he' b v) = e' (totalSpaceMk b (e.symm b v)) :=
+  by
+  ext
+  · rw [e.mk_symm hb.1 v, e'.coe_fst', e.proj_symm_apply' hb.1]
+    rw [e.proj_symm_apply' hb.1]
+    exact hb.2
+  · exact a.smooth_coord_change_apply he he' hb v
+#align vector_prebundle.mk_smooth_coord_change VectorPrebundle.mk_smoothCoordChange
+
+variable (IB)
+
+/-- Make a `smooth_vector_bundle` from a `smooth_vector_prebundle`.  -/
+theorem smoothVectorBundle :
+    @SmoothVectorBundle _ _ F E _ _ _ _ _ _ IB _ _ _ _ _ _ _ a.totalSpaceTopology a.fiberTopology
+      a.toFiberBundle a.to_vectorBundle :=
+  {
+    smoothOn_coord_change := by
+      rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩
+      refine' (a.smooth_on_smooth_coord_change he he').congr _
+      intro b hb
+      ext v
+      rw [a.smooth_coord_change_apply he he' hb v, ContinuousLinearEquiv.coe_coe,
+        Trivialization.coordChangeL_apply]
+      exacts[rfl, hb] }
+#align vector_prebundle.smooth_vector_bundle VectorPrebundle.smoothVectorBundle
+
+end VectorPrebundle
+

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -332,14 +332,14 @@ namespace VectorBundleCore
 
 variable {ι : Type _} {F} (Z : VectorBundleCore 𝕜 B F ι)
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`smoothOn_coord_change] [] -/
 /-- Mixin for a `vector_bundle_core` stating smoothness (of transition functions). -/
 class IsSmooth (IB : ModelWithCorners 𝕜 EB HB) : Prop where
   smoothOn_coord_change :
     ∀ i j, SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (Z.coordChange i j) (Z.baseSet i ∩ Z.baseSet j)
 #align vector_bundle_core.is_smooth VectorBundleCore.IsSmooth
 
-/- ./././Mathport/Syntax/Translate/Command.lean:234:13: unsupported: advanced export style -/
+/- ./././Mathport/Syntax/Translate/Command.lean:239:13: unsupported: advanced export style -/
 export IsSmooth ()
 
 variable [Z.IsSmooth IB]

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -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.basic
-! leanprover-community/mathlib commit ddec54a71a0dd025c05445d467f1a2b7d586a3ba
+! leanprover-community/mathlib commit 0187644979f2d3e10a06e916a869c994facd9a87
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -62,7 +62,11 @@ assert_not_exists mfderiv
 
 open Bundle Set LocalHomeomorph
 
-open Manifold Bundle
+open Function (id_def)
+
+open Filter
+
+open Manifold Bundle Topology
 
 variable {𝕜 B B' F M : Type _} {E : B → Type _}
 
@@ -107,6 +111,148 @@ theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
   rw [Trivialization.coe_coe, Trivialization.coe_fst' _ (mem_base_set_trivialization_at F E x.proj)]
 #align fiber_bundle.charted_space_chart_at FiberBundle.chartedSpace_chartAt
 
+theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace E) (y : ModelProd HB F)
+    (hy : y ∈ (chartAt (ModelProd HB F) x).target) :
+    ((chartAt (ModelProd HB F) x).symm y).proj = (chartAt HB x.proj).symm y.1 :=
+  by
+  simp only [FiberBundle.chartedSpace_chartAt, mfld_simps] at hy⊢
+  exact (trivialization_at F E x.proj).proj_symm_apply hy.2
+#align fiber_bundle.charted_space_chart_at_symm_fst FiberBundle.chartedSpace_chartAt_symm_fst
+
+end
+
+section
+
+variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+  [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)] {EB : Type _}
+  [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type _} [TopologicalSpace HB]
+  (IB : ModelWithCorners 𝕜 EB HB) (E' : B → Type _) [∀ x, Zero (E' x)] {EM : Type _}
+  [NormedAddCommGroup EM] [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM]
+  {IM : ModelWithCorners 𝕜 EM HM} [TopologicalSpace M] [ChartedSpace HM M]
+  [Is : SmoothManifoldWithCorners IM M] {n : ℕ∞}
+
+variable [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
+
+protected theorem FiberBundle.extChartAt (x : TotalSpace E) :
+    extChartAt (IB.Prod 𝓘(𝕜, F)) x =
+      (trivializationAt F E x.proj).toLocalEquiv ≫
+        (extChartAt IB x.proj).Prod (LocalEquiv.refl F) :=
+  by
+  simp_rw [extChartAt, FiberBundle.chartedSpace_chartAt, extend]
+  simp only [LocalEquiv.trans_assoc, mfld_simps]
+#align fiber_bundle.ext_chart_at FiberBundle.extChartAt
+
+/-! ### Smoothness of maps in/out fiber bundles
+
+Note: For these results we don't need that the bundle is a smooth vector bundle, or even a vector
+bundle at all, just that it is a fiber bundle over a charted base space.
+-/
+
+
+namespace Bundle
+
+variable {F E IB}
+
+/-- Characterization of C^n functions into a smooth vector bundle. -/
+theorem contMdiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀ : M} :
+    ContMdiffWithinAt IM (IB.Prod 𝓘(𝕜, F)) n f s x₀ ↔
+      ContMdiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
+        ContMdiffWithinAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) s x₀ :=
+  by
+  simp (config := { singlePass := true }) only [contMdiffWithinAt_iff_target]
+  rw [and_and_and_comm, ← continuous_within_at_total_space, and_congr_right_iff]
+  intro hf
+  simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp, LocalEquiv.trans_apply,
+    LocalEquiv.prod_coe, LocalEquiv.refl_coe, extChartAt_self_apply, modelWithCornersSelf_coe,
+    id_def]
+  refine' (contMdiffWithinAt_prod_iff _).trans _
+  -- rw doesn't do this?
+  have h1 : (fun x => (f x).proj) ⁻¹' (trivialization_at F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
+    ((continuous_proj F E).ContinuousWithinAt.comp hf (maps_to_image f s)).preimage_mem_nhdsWithin
+      ((Trivialization.open_baseSet _).mem_nhds (mem_base_set_trivialization_at F E _))
+  refine'
+    and_congr (eventually_eq.cont_mdiff_within_at_iff (eventually_of_mem h1 fun x hx => _) _)
+      Iff.rfl
+  · simp_rw [Function.comp, LocalHomeomorph.coe_coe, Trivialization.coe_coe]
+    rw [Trivialization.coe_fst']
+    exact hx
+  · simp only [mfld_simps]
+#align bundle.cont_mdiff_within_at_total_space Bundle.contMdiffWithinAt_totalSpace
+
+/-- Characterization of C^n functions into a smooth vector bundle. -/
+theorem contMdiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
+    ContMdiffAt IM (IB.Prod 𝓘(𝕜, F)) n f x₀ ↔
+      ContMdiffAt IM IB n (fun x => (f x).proj) x₀ ∧
+        ContMdiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ :=
+  by
+  simp_rw [← contMdiffWithinAt_univ]
+  exact cont_mdiff_within_at_total_space f
+#align bundle.cont_mdiff_at_total_space Bundle.contMdiffAt_totalSpace
+
+variable (E)
+
+theorem contMdiff_proj : ContMdiff (IB.Prod 𝓘(𝕜, F)) IB n (π E) :=
+  by
+  intro x
+  rw [ContMdiffAt, contMdiffWithinAt_iff']
+  refine' ⟨(continuous_proj F E).ContinuousWithinAt, _⟩
+  simp_rw [(· ∘ ·), FiberBundle.extChartAt]
+  apply cont_diff_within_at_fst.congr
+  · rintro ⟨a, b⟩ hab
+    simp only [mfld_simps] at hab
+    have : ((chart_at HB x.1).symm (IB.symm a), b) ∈ (trivialization_at F E x.fst).target := by
+      simp only [hab, mfld_simps]
+    simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
+  · simp only [mfld_simps]
+#align bundle.cont_mdiff_proj Bundle.contMdiff_proj
+
+theorem smooth_proj : Smooth (IB.Prod 𝓘(𝕜, F)) IB (π E) :=
+  contMdiff_proj E
+#align bundle.smooth_proj Bundle.smooth_proj
+
+theorem contMdiffOn_proj {s : Set (TotalSpace E)} : ContMdiffOn (IB.Prod 𝓘(𝕜, F)) IB n (π E) s :=
+  (Bundle.contMdiff_proj E).ContMdiffOn
+#align bundle.cont_mdiff_on_proj Bundle.contMdiffOn_proj
+
+theorem smoothOn_proj {s : Set (TotalSpace E)} : SmoothOn (IB.Prod 𝓘(𝕜, F)) IB (π E) s :=
+  contMdiffOn_proj E
+#align bundle.smooth_on_proj Bundle.smoothOn_proj
+
+theorem contMdiffAt_proj {p : TotalSpace E} : ContMdiffAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) p :=
+  (Bundle.contMdiff_proj E).ContMdiffAt
+#align bundle.cont_mdiff_at_proj Bundle.contMdiffAt_proj
+
+theorem smoothAt_proj {p : TotalSpace E} : SmoothAt (IB.Prod 𝓘(𝕜, F)) IB (π E) p :=
+  Bundle.contMdiffAt_proj E
+#align bundle.smooth_at_proj Bundle.smoothAt_proj
+
+theorem contMdiffWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
+    ContMdiffWithinAt (IB.Prod 𝓘(𝕜, F)) IB n (π E) s p :=
+  (Bundle.contMdiffAt_proj E).ContMdiffWithinAt
+#align bundle.cont_mdiff_within_at_proj Bundle.contMdiffWithinAt_proj
+
+theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
+    SmoothWithinAt (IB.Prod 𝓘(𝕜, F)) IB (π E) s p :=
+  Bundle.contMdiffWithinAt_proj E
+#align bundle.smooth_within_at_proj Bundle.smoothWithinAt_proj
+
+variable (𝕜 E) [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [VectorBundle 𝕜 F E]
+
+theorem smooth_zeroSection : Smooth IB (IB.Prod 𝓘(𝕜, F)) (zeroSection E) :=
+  by
+  intro x
+  rw [Bundle.contMdiffAt_totalSpace]
+  refine' ⟨contMdiffAt_id, cont_mdiff_at_const.congr_of_eventually_eq _⟩
+  · exact 0
+  refine'
+    eventually_of_mem
+      ((trivialization_at F E x).open_baseSet.mem_nhds (mem_base_set_trivialization_at F E x))
+      fun x' hx' => _
+  simp_rw [zero_section_proj, (trivialization_at F E x).zeroSection 𝕜 hx']
+#align bundle.smooth_zero_section Bundle.smooth_zeroSection
+
+end Bundle
+
 end
 
 /-! ### Smooth vector bundles -/
@@ -116,7 +262,9 @@ variable [NontriviallyNormedField 𝕜] [∀ x, AddCommMonoid (E x)] [∀ x, Mod
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace (TotalSpace E)]
   [∀ x, TopologicalSpace (E x)] {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB]
   {HB : Type _} [TopologicalSpace HB] (IB : ModelWithCorners 𝕜 EB HB) [TopologicalSpace B]
-  [ChartedSpace HB B] [SmoothManifoldWithCorners IB B]
+  [ChartedSpace HB B] [SmoothManifoldWithCorners IB B] {EM : Type _} [NormedAddCommGroup EM]
+  [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
+  [TopologicalSpace M] [ChartedSpace HM M] [Is : SmoothManifoldWithCorners IM M] {n : ℕ∞}
 
 variable (F E) [FiberBundle F E] [VectorBundle 𝕜 F E]
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -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.basic
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit ddec54a71a0dd025c05445d467f1a2b7d586a3ba
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -72,11 +72,11 @@ variable {𝕜 B B' F M : Type _} {E : B → Type _}
 section
 
 variable [TopologicalSpace F] [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
-  {HB : Type _} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B]
+  {HB : Type _} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
 /-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
 `B × F`. -/
-instance FiberBundle.chartedSpace [FiberBundle F E] : ChartedSpace (B × F) (TotalSpace E)
+instance FiberBundle.chartedSpace : ChartedSpace (B × F) (TotalSpace E)
     where
   atlas := (fun e : Trivialization F (π E) => e.toLocalHomeomorph) '' trivializationAtlas F E
   chartAt x := (trivializationAt F E x.proj).toLocalHomeomorph
@@ -85,17 +85,30 @@ instance FiberBundle.chartedSpace [FiberBundle F E] : ChartedSpace (B × F) (Tot
   chart_mem_atlas x := mem_image_of_mem _ (trivialization_mem_atlas F E _)
 #align fiber_bundle.charted_space FiberBundle.chartedSpace
 
+section
+
 attribute [local reducible] ModelProd
 
 /-- Let `B` be a charted space modelled on `HB`.  Then a fiber bundle `E` over a base `B` with model
 fiber `F` is naturally a charted space modelled on `HB.prod F`. -/
-instance FiberBundle.chartedSpace' [FiberBundle F E] :
-    ChartedSpace (ModelProd HB F) (TotalSpace E) :=
+instance FiberBundle.chartedSpace' : ChartedSpace (ModelProd HB F) (TotalSpace E) :=
   ChartedSpace.comp _ (ModelProd B F) _
 #align fiber_bundle.charted_space' FiberBundle.chartedSpace'
 
 end
 
+theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
+    chartAt (ModelProd HB F) x =
+      (trivializationAt F E x.proj).toLocalHomeomorph ≫ₕ
+        (chartAt HB x.proj).Prod (LocalHomeomorph.refl F) :=
+  by
+  dsimp only [FiberBundle.chartedSpace', ChartedSpace.comp, FiberBundle.chartedSpace,
+    prodChartedSpace, chartedSpaceSelf]
+  rw [Trivialization.coe_coe, Trivialization.coe_fst' _ (mem_base_set_trivialization_at F E x.proj)]
+#align fiber_bundle.charted_space_chart_at FiberBundle.chartedSpace_chartAt
+
+end
+
 /-! ### Smooth vector bundles -/
 
 

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

• Also redefine MDifferentiableWithinAt and MDifferentiableAt so that they are using LiftProp[Within]At.
• This causes a speedup in the old proof of ContMDiffWithinAt.cle_arrowCongr by 25%.
• Also give some extra information in the proof of ContMDiffWithinAt.cle_arrowCongr to speed it up by another factor of 4.
• A bit of the fallout (e.g. in hasSmoothAddSelf) is from Lean unfolding way too many definitions to make things definitionally equal. Since LiftPropWithinAt is now a structure, the old proofs now break, unless you rewrite with chartedSpaceSelf_prod), causing much less defeq-abuse.
• The new lemmas MDifferentiableWithinAt.differentiableWithinAt_writtenInExtChartAt and MDifferentiableAt.differentiableWithinAt_writtenInExtChartAt have a bit long names. This is to avoid naming clash with the existing MDifferentiableWithinAt.differentiableWithinAt. I'm open for other suggestions.

@@ -183,8 +183,8 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x
   rw [and_and_and_comm, ← FiberBundle.continuousWithinAt_totalSpace, and_congr_right_iff]
   intro hf
   simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp,
-    PartialEquiv.trans_apply, PartialEquiv.prod_coe, PartialEquiv.refl_coe, extChartAt_self_apply,
-    modelWithCornersSelf_coe, Function.id_def]
+    PartialEquiv.trans_apply, PartialEquiv.prod_coe, PartialEquiv.refl_coe,
+    extChartAt_self_apply, modelWithCornersSelf_coe, Function.id_def, ← chartedSpaceSelf_prod]
   refine (contMDiffWithinAt_prod_iff _).trans (and_congr ?_ Iff.rfl)
   have h1 : (fun x => (f x).proj) ⁻¹' (trivializationAt F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
     ((FiberBundle.continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s))

In all cases, the original proof fixed itself.

@@ -594,9 +594,7 @@ is a smooth vector bundle. -/
 instance smoothVectorBundle : SmoothVectorBundle F Z.Fiber IB where
   smoothOn_coordChangeL := by
     rintro - - ⟨i, rfl⟩ ⟨i', rfl⟩
-    -- Porting note: Originally `Z.smoothOn_coordChange IB i i'`
-    refine'
-      (VectorBundleCore.IsSmooth.smoothOn_coordChange (Z := Z) (IB := IB) i i').congr fun b hb => _
+    refine (Z.smoothOn_coordChange IB i i').congr fun b hb ↦ ?_
     ext v
     exact Z.localTriv_coordChange_eq i i' hb v
 #align vector_bundle_core.smooth_vector_bundle VectorBundleCore.smoothVectorBundle

Some small changes to adapt to the 2024-03-16 nightly that can land in advance.

@@ -184,7 +184,7 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x
   intro hf
   simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp,
     PartialEquiv.trans_apply, PartialEquiv.prod_coe, PartialEquiv.refl_coe, extChartAt_self_apply,
-    modelWithCornersSelf_coe, id_def]
+    modelWithCornersSelf_coe, Function.id_def]
   refine (contMDiffWithinAt_prod_iff _).trans (and_congr ?_ Iff.rfl)
   have h1 : (fun x => (f x).proj) ⁻¹' (trivializationAt F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
     ((FiberBundle.continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s))

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)

@@ -279,7 +279,6 @@ variable [NontriviallyNormedField 𝕜] {EB : Type*} [NormedAddCommGroup EB] [No
 section WithTopology
 
 variable [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)] (F E)
-
 variable [FiberBundle F E] [VectorBundle 𝕜 F E]
 
 /-- When `B` is a smooth manifold with corners with respect to a model `IB` and `E` is a

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".

@@ -141,7 +141,7 @@ protected theorem FiberBundle.extChartAt (x : TotalSpace F E) :
         (extChartAt IB x.proj).prod (PartialEquiv.refl F) := by
   simp_rw [extChartAt, FiberBundle.chartedSpace_chartAt, extend]
   simp only [PartialEquiv.trans_assoc, mfld_simps]
-  -- porting note: should not be needed
+  -- Porting note: should not be needed
   rw [PartialEquiv.prod_trans, PartialEquiv.refl_trans]
 #align fiber_bundle.ext_chart_at FiberBundle.extChartAt
 

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -438,9 +438,9 @@ theorem Trivialization.contMDiffOn_symm_trans :
     (contMDiffOn_fst.coordChange contMDiffOn_snd Hmaps.1 Hmaps.2)).congr ?_
   rintro ⟨b, x⟩ hb
   refine Prod.ext ?_ rfl
-  · have : (e.toPartialHomeomorph.symm (b, x)).1 ∈ e'.baseSet
-    · simp_all only [Trivialization.mem_target, mfld_simps]
-    exact (e'.coe_fst' this).trans (e.proj_symm_apply hb.1)
+  have : (e.toPartialHomeomorph.symm (b, x)).1 ∈ e'.baseSet := by
+    simp_all only [Trivialization.mem_target, mfld_simps]
+  exact (e'.coe_fst' this).trans (e.proj_symm_apply hb.1)
 
 variable {IB e e'}
 

After this PR, no file in Geometry uses autoImplicit, and in Analysis it's scoped to six declarations.

@@ -59,9 +59,6 @@ fields, they can also be C^k vector bundles, etc.
   bundle.
 -/
 
-set_option autoImplicit true
-
-
 assert_not_exists mfderiv
 
 open Bundle Set PartialHomeomorph
@@ -328,58 +325,59 @@ theorem contMDiffOn_symm_coordChangeL :
 
 variable {e e'}
 
-theorem contMDiffAt_coordChangeL (h : x ∈ e.baseSet) (h' : x ∈ e'.baseSet) :
+theorem contMDiffAt_coordChangeL {x : B} (h : x ∈ e.baseSet) (h' : x ∈ e'.baseSet) :
     ContMDiffAt IB 𝓘(𝕜, F →L[𝕜] F) n (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F)) x :=
   (contMDiffOn_coordChangeL IB e e').contMDiffAt <|
     (e.open_baseSet.inter e'.open_baseSet).mem_nhds ⟨h, h'⟩
 
-theorem smoothAt_coordChangeL (h : x ∈ e.baseSet) (h' : x ∈ e'.baseSet) :
+theorem smoothAt_coordChangeL {x : B} (h : x ∈ e.baseSet) (h' : x ∈ e'.baseSet) :
     SmoothAt IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F)) x :=
   contMDiffAt_coordChangeL IB h h'
 
 variable {IB}
+variable {s : Set M} {f : M → B} {g : M → F} {x : M}
 
-protected theorem ContMDiffWithinAt.coordChangeL {f : M → B}
+protected theorem ContMDiffWithinAt.coordChangeL
     (hf : ContMDiffWithinAt IM IB n f s x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     ContMDiffWithinAt IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s x :=
   (contMDiffAt_coordChangeL IB he he').comp_contMDiffWithinAt _ hf
 
-protected nonrec theorem ContMDiffAt.coordChangeL {f : M → B}
+protected nonrec theorem ContMDiffAt.coordChangeL
     (hf : ContMDiffAt IM IB n f x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     ContMDiffAt IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) x :=
   hf.coordChangeL he he'
 
-protected theorem ContMDiffOn.coordChangeL {f : M → B}
+protected theorem ContMDiffOn.coordChangeL
     (hf : ContMDiffOn IM IB n f s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
     ContMDiffOn IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s :=
   fun x hx ↦ (hf x hx).coordChangeL (he hx) (he' hx)
 
-protected theorem ContMDiff.coordChangeL {f : M → B}
+protected theorem ContMDiff.coordChangeL
     (hf : ContMDiff IM IB n f) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
     ContMDiff IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) := fun x ↦
   (hf x).coordChangeL (he x) (he' x)
 
-protected nonrec theorem SmoothWithinAt.coordChangeL {f : M → B}
+protected nonrec theorem SmoothWithinAt.coordChangeL
     (hf : SmoothWithinAt IM IB f s x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     SmoothWithinAt IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s x :=
   hf.coordChangeL he he'
 
-protected nonrec theorem SmoothAt.coordChangeL {f : M → B}
+protected nonrec theorem SmoothAt.coordChangeL
     (hf : SmoothAt IM IB f x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     SmoothAt IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) x :=
   hf.coordChangeL he he'
 
-protected nonrec theorem SmoothOn.coordChangeL {f : M → B}
+protected nonrec theorem SmoothOn.coordChangeL
     (hf : SmoothOn IM IB f s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
     SmoothOn IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s :=
   hf.coordChangeL he he'
 
-protected nonrec theorem Smooth.coordChangeL {f : M → B}
+protected nonrec theorem Smooth.coordChangeL
     (hf : Smooth IM IB f) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
     Smooth IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) :=
   hf.coordChangeL he he'
 
-protected theorem ContMDiffWithinAt.coordChange {f : M → B} {g : M → F}
+protected theorem ContMDiffWithinAt.coordChange
     (hf : ContMDiffWithinAt IM IB n f s x) (hg : ContMDiffWithinAt IM 𝓘(𝕜, F) n g s x)
     (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) s x := by
@@ -390,39 +388,39 @@ protected theorem ContMDiffWithinAt.coordChange {f : M → B} {g : M → F}
     exact (Trivialization.coordChangeL_apply' e e' hy (g y)).symm
   · exact (Trivialization.coordChangeL_apply' e e' ⟨he, he'⟩ (g x)).symm
 
-protected nonrec theorem ContMDiffAt.coordChange {f : M → B} {g : M → F}
+protected nonrec theorem ContMDiffAt.coordChange
     (hf : ContMDiffAt IM IB n f x) (hg : ContMDiffAt IM 𝓘(𝕜, F) n g x) (he : f x ∈ e.baseSet)
     (he' : f x ∈ e'.baseSet) :
     ContMDiffAt IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) x :=
   hf.coordChange hg he he'
 
-protected theorem ContMDiffOn.coordChange {f : M → B} {g : M → F} (hf : ContMDiffOn IM IB n f s)
+protected theorem ContMDiffOn.coordChange (hf : ContMDiffOn IM IB n f s)
     (hg : ContMDiffOn IM 𝓘(𝕜, F) n g s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
     ContMDiffOn IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) s := fun x hx ↦
   (hf x hx).coordChange (hg x hx) (he hx) (he' hx)
 
-protected theorem ContMDiff.coordChange {f : M → B} {g : M → F} (hf : ContMDiff IM IB n f)
+protected theorem ContMDiff.coordChange (hf : ContMDiff IM IB n f)
     (hg : ContMDiff IM 𝓘(𝕜, F) n g) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
     ContMDiff IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) := fun x ↦
   (hf x).coordChange (hg x) (he x) (he' x)
 
-protected nonrec theorem SmoothWithinAt.coordChange {f : M → B} {g : M → F}
+protected nonrec theorem SmoothWithinAt.coordChange
     (hf : SmoothWithinAt IM IB f s x) (hg : SmoothWithinAt IM 𝓘(𝕜, F) g s x)
     (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     SmoothWithinAt IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) s x :=
   hf.coordChange hg he he'
 
-protected nonrec theorem SmoothAt.coordChange {f : M → B} {g : M → F} (hf : SmoothAt IM IB f x)
+protected nonrec theorem SmoothAt.coordChange (hf : SmoothAt IM IB f x)
     (hg : SmoothAt IM 𝓘(𝕜, F) g x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
     SmoothAt IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) x :=
   hf.coordChange hg he he'
 
-protected nonrec theorem SmoothOn.coordChange {f : M → B} {g : M → F} (hf : SmoothOn IM IB f s)
+protected nonrec theorem SmoothOn.coordChange (hf : SmoothOn IM IB f s)
     (hg : SmoothOn IM 𝓘(𝕜, F) g s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
     SmoothOn IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) s :=
   hf.coordChange hg he he'
 
-protected theorem Smooth.coordChange {f : M → B} {g : M → F} (hf : Smooth IM IB f)
+protected theorem Smooth.coordChange (hf : Smooth IM IB f)
     (hg : Smooth IM 𝓘(𝕜, F) g) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
     Smooth IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) := fun x ↦
   (hf x).coordChange (hg x) (he x) (he' x)

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

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

@@ -479,7 +479,7 @@ instance SmoothFiberwiseLinear.hasGroupoid :
     refine' ⟨_, _, e.open_baseSet.inter e'.open_baseSet, smoothOn_coordChangeL IB e e',
       smoothOn_symm_coordChangeL IB e e', _⟩
     refine PartialHomeomorph.eqOnSourceSetoid.symm ⟨?_, ?_⟩
-    · simp only [e.symm_trans_source_eq e', FiberwiseLinear.localHomeomorph, trans_toPartialEquiv,
+    · simp only [e.symm_trans_source_eq e', FiberwiseLinear.partialHomeomorph, trans_toPartialEquiv,
         symm_toPartialEquiv]
     · rintro ⟨b, v⟩ hb
       exact (e.apply_symm_apply_eq_coordChangeL e' hb.1 v).symm

Almost all of them should speak about partial homeomorphisms instead. In two cases, I decided removing the "local" was clearer than adding "partial".

Follow-up to #8982; complements #9238.

@@ -20,7 +20,7 @@ is also a charted space over `H × F`.
 
 Now, we define `SmoothVectorBundle` as the `Prop` of having smooth transition functions.
 Recall the structure groupoid `smoothFiberwiseLinear` on `B × F` consisting of smooth, fiberwise
-linear local homeomorphisms.  We show that our definition of "smooth vector bundle" implies
+linear partial homeomorphisms.  We show that our definition of "smooth vector bundle" implies
 `HasGroupoid` for this groupoid, and show (by a "composition" of `HasGroupoid` instances) that
 this means that a smooth vector bundle is a smooth manifold.
 

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>

@@ -140,19 +140,19 @@ variable [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
 protected theorem FiberBundle.extChartAt (x : TotalSpace F E) :
     extChartAt (IB.prod 𝓘(𝕜, F)) x =
-      (trivializationAt F E x.proj).toLocalEquiv ≫
-        (extChartAt IB x.proj).prod (LocalEquiv.refl F) := by
+      (trivializationAt F E x.proj).toPartialEquiv ≫
+        (extChartAt IB x.proj).prod (PartialEquiv.refl F) := by
   simp_rw [extChartAt, FiberBundle.chartedSpace_chartAt, extend]
-  simp only [LocalEquiv.trans_assoc, mfld_simps]
+  simp only [PartialEquiv.trans_assoc, mfld_simps]
   -- porting note: should not be needed
-  rw [LocalEquiv.prod_trans, LocalEquiv.refl_trans]
+  rw [PartialEquiv.prod_trans, PartialEquiv.refl_trans]
 #align fiber_bundle.ext_chart_at FiberBundle.extChartAt
 
 protected theorem FiberBundle.extChartAt_target (x : TotalSpace F E) :
     (extChartAt (IB.prod 𝓘(𝕜, F)) x).target =
       ((extChartAt IB x.proj).target ∩
         (extChartAt IB x.proj).symm ⁻¹' (trivializationAt F E x.proj).baseSet) ×ˢ univ := by
-  rw [FiberBundle.extChartAt, LocalEquiv.trans_target, Trivialization.target_eq, inter_prod]
+  rw [FiberBundle.extChartAt, PartialEquiv.trans_target, Trivialization.target_eq, inter_prod]
   rfl
 
 theorem FiberBundle.writtenInExtChartAt_trivializationAt {x : TotalSpace F E} {y}
@@ -185,9 +185,9 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x
   simp (config := { singlePass := true }) only [contMDiffWithinAt_iff_target]
   rw [and_and_and_comm, ← FiberBundle.continuousWithinAt_totalSpace, and_congr_right_iff]
   intro hf
-  simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp, LocalEquiv.trans_apply,
-    LocalEquiv.prod_coe, LocalEquiv.refl_coe, extChartAt_self_apply, modelWithCornersSelf_coe,
-    id_def]
+  simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp,
+    PartialEquiv.trans_apply, PartialEquiv.prod_coe, PartialEquiv.refl_coe, extChartAt_self_apply,
+    modelWithCornersSelf_coe, id_def]
   refine (contMDiffWithinAt_prod_iff _).trans (and_congr ?_ Iff.rfl)
   have h1 : (fun x => (f x).proj) ⁻¹' (trivializationAt F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
     ((FiberBundle.continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s))
@@ -479,8 +479,8 @@ instance SmoothFiberwiseLinear.hasGroupoid :
     refine' ⟨_, _, e.open_baseSet.inter e'.open_baseSet, smoothOn_coordChangeL IB e e',
       smoothOn_symm_coordChangeL IB e e', _⟩
     refine PartialHomeomorph.eqOnSourceSetoid.symm ⟨?_, ?_⟩
-    · simp only [e.symm_trans_source_eq e', FiberwiseLinear.localHomeomorph, trans_toLocalEquiv,
-        symm_toLocalEquiv]
+    · simp only [e.symm_trans_source_eq e', FiberwiseLinear.localHomeomorph, trans_toPartialEquiv,
+        symm_toPartialEquiv]
     · rintro ⟨b, v⟩ hb
       exact (e.apply_symm_apply_eq_coordChangeL e' hb.1 v).symm
 #align smooth_fiberwise_linear.has_groupoid SmoothFiberwiseLinear.hasGroupoid

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

@@ -64,7 +64,7 @@ set_option autoImplicit true
 
 assert_not_exists mfderiv
 
-open Bundle Set LocalHomeomorph
+open Bundle Set PartialHomeomorph
 
 open Function (id_def)
 
@@ -85,15 +85,15 @@ variable [TopologicalSpace F] [TopologicalSpace (TotalSpace F E)] [∀ x, Topolo
 /-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
 `B × F`. -/
 instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace F E) where
-  atlas := (fun e : Trivialization F (π F E) => e.toLocalHomeomorph) '' trivializationAtlas F E
-  chartAt x := (trivializationAt F E x.proj).toLocalHomeomorph
+  atlas := (fun e : Trivialization F (π F E) => e.toPartialHomeomorph) '' trivializationAtlas F E
+  chartAt x := (trivializationAt F E x.proj).toPartialHomeomorph
   mem_chart_source x :=
     (trivializationAt F E x.proj).mem_source.mpr (mem_baseSet_trivializationAt F E x.proj)
   chart_mem_atlas _ := mem_image_of_mem _ (trivialization_mem_atlas F E _)
 #align fiber_bundle.charted_space FiberBundle.chartedSpace'
 
 theorem FiberBundle.chartedSpace'_chartAt (x : TotalSpace F E) :
-    chartAt (B × F) x = (trivializationAt F E x.proj).toLocalHomeomorph :=
+    chartAt (B × F) x = (trivializationAt F E x.proj).toPartialHomeomorph :=
   rfl
 
 /- Porting note: In Lean 3, the next instance was inside a section with locally reducible
@@ -110,8 +110,8 @@ instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace F
 
 theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace F E) :
     chartAt (ModelProd HB F) x =
-      (trivializationAt F E x.proj).toLocalHomeomorph ≫ₕ
-        (chartAt HB x.proj).prod (LocalHomeomorph.refl F) := by
+      (trivializationAt F E x.proj).toPartialHomeomorph ≫ₕ
+        (chartAt HB x.proj).prod (PartialHomeomorph.refl F) := by
   dsimp only [chartAt_comp, prodChartedSpace_chartAt, FiberBundle.chartedSpace'_chartAt,
     chartAt_self_eq]
   rw [Trivialization.coe_coe, Trivialization.coe_fst' _ (mem_baseSet_trivializationAt F E x.proj)]
@@ -164,7 +164,7 @@ theorem FiberBundle.writtenInExtChartAt_trivializationAt {x : TotalSpace F E} {y
 theorem FiberBundle.writtenInExtChartAt_trivializationAt_symm {x : TotalSpace F E} {y}
     (hy : y ∈ (extChartAt (IB.prod 𝓘(𝕜, F)) x).target) :
     writtenInExtChartAt (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) (trivializationAt F E x.proj x)
-      (trivializationAt F E x.proj).toLocalHomeomorph.symm y = y :=
+      (trivializationAt F E x.proj).toPartialHomeomorph.symm y = y :=
   writtenInExtChartAt_chartAt_symm_comp _ _ hy
 
 /-! ### Smoothness of maps in/out fiber bundles
@@ -193,7 +193,7 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x
     ((FiberBundle.continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s))
       ((Trivialization.open_baseSet _).mem_nhds (mem_baseSet_trivializationAt F E _))
   refine EventuallyEq.contMDiffWithinAt_iff (eventually_of_mem h1 fun x hx => ?_) ?_
-  · simp_rw [Function.comp, LocalHomeomorph.coe_coe, Trivialization.coe_coe]
+  · simp_rw [Function.comp, PartialHomeomorph.coe_coe, Trivialization.coe_coe]
     rw [Trivialization.coe_fst']
     exact hx
   · simp only [mfld_simps]
@@ -431,7 +431,7 @@ variable (IB e e')
 
 theorem Trivialization.contMDiffOn_symm_trans :
     ContMDiffOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) n
-      (e.toLocalHomeomorph.symm ≫ₕ e'.toLocalHomeomorph) (e.target ∩ e'.target) := by
+      (e.toPartialHomeomorph.symm ≫ₕ e'.toPartialHomeomorph) (e.target ∩ e'.target) := by
   have Hmaps : MapsTo Prod.fst (e.target ∩ e'.target) (e.baseSet ∩ e'.baseSet) := fun x hx ↦
     ⟨e.mem_target.1 hx.1, e'.mem_target.1 hx.2⟩
   rw [mapsTo_inter] at Hmaps
@@ -440,7 +440,7 @@ theorem Trivialization.contMDiffOn_symm_trans :
     (contMDiffOn_fst.coordChange contMDiffOn_snd Hmaps.1 Hmaps.2)).congr ?_
   rintro ⟨b, x⟩ hb
   refine Prod.ext ?_ rfl
-  · have : (e.toLocalHomeomorph.symm (b, x)).1 ∈ e'.baseSet
+  · have : (e.toPartialHomeomorph.symm (b, x)).1 ∈ e'.baseSet
     · simp_all only [Trivialization.mem_target, mfld_simps]
     exact (e'.coe_fst' this).trans (e.proj_symm_apply hb.1)
 
@@ -478,7 +478,7 @@ instance SmoothFiberwiseLinear.hasGroupoid :
     rw [mem_smoothFiberwiseLinear_iff]
     refine' ⟨_, _, e.open_baseSet.inter e'.open_baseSet, smoothOn_coordChangeL IB e e',
       smoothOn_symm_coordChangeL IB e e', _⟩
-    refine LocalHomeomorph.eqOnSourceSetoid.symm ⟨?_, ?_⟩
+    refine PartialHomeomorph.eqOnSourceSetoid.symm ⟨?_, ?_⟩
     · simp only [e.symm_trans_source_eq e', FiberwiseLinear.localHomeomorph, trans_toLocalEquiv,
         symm_toLocalEquiv]
     · rintro ⟨b, v⟩ hb
@@ -566,8 +566,8 @@ theorem Trivialization.smoothOn (e : Trivialization F (π F E)) [MemTrivializati
   exact (this.1.prod_mk this.2).congr fun x hx ↦ (e.mk_proj_snd hx).symm
 
 theorem Trivialization.smoothOn_symm (e : Trivialization F (π F E)) [MemTrivializationAtlas e] :
-    SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) e.toLocalHomeomorph.symm e.target := by
-  rw [e.smoothOn_iff IB e.toLocalHomeomorph.symm_mapsTo]
+    SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) e.toPartialHomeomorph.symm e.target := by
+  rw [e.smoothOn_iff IB e.toPartialHomeomorph.symm_mapsTo]
   refine ⟨smoothOn_fst.congr fun x hx ↦ e.proj_symm_apply hx, smoothOn_snd.congr fun x hx ↦ ?_⟩
   rw [e.apply_symm_apply hx]
 

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.)

@@ -3,6 +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.Atlas
 import Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear
 import Mathlib.Topology.VectorBundle.Constructions
 

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -58,6 +58,8 @@ fields, they can also be C^k vector bundles, etc.
   bundle.
 -/
 
+set_option autoImplicit true
+
 
 assert_not_exists mfderiv
 

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

This has nice performance benefits.

@@ -69,7 +69,7 @@ open Filter
 
 open scoped Manifold Bundle Topology
 
-variable {𝕜 B B' F M : Type _} {E : B → Type _}
+variable {𝕜 B B' F M : Type*} {E : B → Type*}
 
 /-! ### Charted space structure on a fiber bundle -/
 
@@ -77,7 +77,7 @@ variable {𝕜 B B' F M : Type _} {E : B → Type _}
 section
 
 variable [TopologicalSpace F] [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)]
-  {HB : Type _} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
+  {HB : Type*} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
 /-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
 `B × F`. -/
@@ -126,10 +126,10 @@ end
 section
 
 variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-  [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)] {EB : Type _}
-  [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type _} [TopologicalSpace HB]
-  (IB : ModelWithCorners 𝕜 EB HB) (E' : B → Type _) [∀ x, Zero (E' x)] {EM : Type _}
-  [NormedAddCommGroup EM] [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM]
+  [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)] {EB : Type*}
+  [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type*} [TopologicalSpace HB]
+  (IB : ModelWithCorners 𝕜 EB HB) (E' : B → Type*) [∀ x, Zero (E' x)] {EM : Type*}
+  [NormedAddCommGroup EM] [NormedSpace 𝕜 EM] {HM : Type*} [TopologicalSpace HM]
   {IM : ModelWithCorners 𝕜 EM HM} [TopologicalSpace M] [ChartedSpace HM M]
   [Is : SmoothManifoldWithCorners IM M] {n : ℕ∞}
 
@@ -269,10 +269,10 @@ end
 /-! ### Smooth vector bundles -/
 
 
-variable [NontriviallyNormedField 𝕜] {EB : Type _} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB]
-  {HB : Type _} [TopologicalSpace HB] (IB : ModelWithCorners 𝕜 EB HB) [TopologicalSpace B]
-  [ChartedSpace HB B] [SmoothManifoldWithCorners IB B] {EM : Type _} [NormedAddCommGroup EM]
-  [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
+variable [NontriviallyNormedField 𝕜] {EB : Type*} [NormedAddCommGroup EB] [NormedSpace 𝕜 EB]
+  {HB : Type*} [TopologicalSpace HB] (IB : ModelWithCorners 𝕜 EB HB) [TopologicalSpace B]
+  [ChartedSpace HB B] [SmoothManifoldWithCorners IB B] {EM : Type*} [NormedAddCommGroup EM]
+  [NormedSpace 𝕜 EM] {HM : Type*} [TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
   [TopologicalSpace M] [ChartedSpace HM M] [Is : SmoothManifoldWithCorners IM M] {n : ℕ∞}
   [∀ x, AddCommMonoid (E x)] [∀ x, Module 𝕜 (E x)] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
@@ -574,7 +574,7 @@ end
 
 namespace VectorBundleCore
 
-variable {ι : Type _} {F}
+variable {ι : Type*} {F}
 variable (Z : VectorBundleCore 𝕜 B F ι)
 
 /-- Mixin for a `VectorBundleCore` stating smoothness (of transition functions). -/
@@ -620,10 +620,10 @@ instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivia
 
 section Prod
 
-variable (F₁ : Type _) [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _)
+variable (F₁ : Type*) [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type*)
   [TopologicalSpace (TotalSpace F₁ E₁)] [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
 
-variable (F₂ : Type _) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type _)
+variable (F₂ : Type*) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type*)
   [TopologicalSpace (TotalSpace F₂ E₂)] [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)]
 
 variable [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)] [FiberBundle F₁ E₁]

@@ -145,13 +145,31 @@ protected theorem FiberBundle.extChartAt (x : TotalSpace F E) :
   rw [LocalEquiv.prod_trans, LocalEquiv.refl_trans]
 #align fiber_bundle.ext_chart_at FiberBundle.extChartAt
 
+protected theorem FiberBundle.extChartAt_target (x : TotalSpace F E) :
+    (extChartAt (IB.prod 𝓘(𝕜, F)) x).target =
+      ((extChartAt IB x.proj).target ∩
+        (extChartAt IB x.proj).symm ⁻¹' (trivializationAt F E x.proj).baseSet) ×ˢ univ := by
+  rw [FiberBundle.extChartAt, LocalEquiv.trans_target, Trivialization.target_eq, inter_prod]
+  rfl
+
+theorem FiberBundle.writtenInExtChartAt_trivializationAt {x : TotalSpace F E} {y}
+    (hy : y ∈ (extChartAt (IB.prod 𝓘(𝕜, F)) x).target) :
+    writtenInExtChartAt (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) x
+      (trivializationAt F E x.proj) y = y :=
+  writtenInExtChartAt_chartAt_comp _ _ hy
+
+theorem FiberBundle.writtenInExtChartAt_trivializationAt_symm {x : TotalSpace F E} {y}
+    (hy : y ∈ (extChartAt (IB.prod 𝓘(𝕜, F)) x).target) :
+    writtenInExtChartAt (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) (trivializationAt F E x.proj x)
+      (trivializationAt F E x.proj).toLocalHomeomorph.symm y = y :=
+  writtenInExtChartAt_chartAt_symm_comp _ _ hy
+
 /-! ### Smoothness of maps in/out fiber bundles
 
 Note: For these results we don't need that the bundle is a smooth vector bundle, or even a vector
 bundle at all, just that it is a fiber bundle over a charted base space.
 -/
 
-
 namespace Bundle
 
 variable {IB}

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 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.basic
-! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear
 import Mathlib.Topology.VectorBundle.Constructions
 
+#align_import geometry.manifold.vector_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-! # Smooth vector bundles
 
 This file defines smooth vector bundles over a smooth manifold.

Forward-port leanprover-community/mathlib#19221

@@ -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.basic
-! leanprover-community/mathlib commit f9ec187127cc5b381dfcf5f4a22dacca4c20b63d
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -79,20 +79,20 @@ variable {𝕜 B B' F M : Type _} {E : B → Type _}
 
 section
 
-variable [TopologicalSpace F] [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)]
+variable [TopologicalSpace F] [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)]
   {HB : Type _} [TopologicalSpace HB] [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
 /-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
 `B × F`. -/
-instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace E) where
-  atlas := (fun e : Trivialization F (π E) => e.toLocalHomeomorph) '' trivializationAtlas F E
+instance FiberBundle.chartedSpace' : ChartedSpace (B × F) (TotalSpace F E) where
+  atlas := (fun e : Trivialization F (π F E) => e.toLocalHomeomorph) '' trivializationAtlas F E
   chartAt x := (trivializationAt F E x.proj).toLocalHomeomorph
   mem_chart_source x :=
     (trivializationAt F E x.proj).mem_source.mpr (mem_baseSet_trivializationAt F E x.proj)
   chart_mem_atlas _ := mem_image_of_mem _ (trivialization_mem_atlas F E _)
 #align fiber_bundle.charted_space FiberBundle.chartedSpace'
 
-theorem FiberBundle.chartedSpace'_chartAt (x : TotalSpace E) :
+theorem FiberBundle.chartedSpace'_chartAt (x : TotalSpace F E) :
     chartAt (B × F) x = (trivializationAt F E x.proj).toLocalHomeomorph :=
   rfl
 
@@ -104,11 +104,11 @@ gives the same instance.
 
 /-- Let `B` be a charted space modelled on `HB`.  Then a fiber bundle `E` over a base `B` with model
 fiber `F` is naturally a charted space modelled on `HB.prod F`. -/
-instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace E) :=
+instance FiberBundle.chartedSpace : ChartedSpace (ModelProd HB F) (TotalSpace F E) :=
   ChartedSpace.comp _ (B × F) _
 #align fiber_bundle.charted_space' FiberBundle.chartedSpace
 
-theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
+theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace F E) :
     chartAt (ModelProd HB F) x =
       (trivializationAt F E x.proj).toLocalHomeomorph ≫ₕ
         (chartAt HB x.proj).prod (LocalHomeomorph.refl F) := by
@@ -117,7 +117,7 @@ theorem FiberBundle.chartedSpace_chartAt (x : TotalSpace E) :
   rw [Trivialization.coe_coe, Trivialization.coe_fst' _ (mem_baseSet_trivializationAt F E x.proj)]
 #align fiber_bundle.charted_space_chart_at FiberBundle.chartedSpace_chartAt
 
-theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace E) (y : ModelProd HB F)
+theorem FiberBundle.chartedSpace_chartAt_symm_fst (x : TotalSpace F E) (y : ModelProd HB F)
     (hy : y ∈ (chartAt (ModelProd HB F) x).target) :
     ((chartAt (ModelProd HB F) x).symm y).proj = (chartAt HB x.proj).symm y.1 := by
   simp only [FiberBundle.chartedSpace_chartAt, mfld_simps] at hy ⊢
@@ -129,7 +129,7 @@ end
 section
 
 variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-  [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)] {EB : Type _}
+  [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)] {EB : Type _}
   [NormedAddCommGroup EB] [NormedSpace 𝕜 EB] {HB : Type _} [TopologicalSpace HB]
   (IB : ModelWithCorners 𝕜 EB HB) (E' : B → Type _) [∀ x, Zero (E' x)] {EM : Type _}
   [NormedAddCommGroup EM] [NormedSpace 𝕜 EM] {HM : Type _} [TopologicalSpace HM]
@@ -138,7 +138,7 @@ variable [NontriviallyNormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜
 
 variable [TopologicalSpace B] [ChartedSpace HB B] [FiberBundle F E]
 
-protected theorem FiberBundle.extChartAt (x : TotalSpace E) :
+protected theorem FiberBundle.extChartAt (x : TotalSpace F E) :
     extChartAt (IB.prod 𝓘(𝕜, F)) x =
       (trivializationAt F E x.proj).toLocalEquiv ≫
         (extChartAt IB x.proj).prod (LocalEquiv.refl F) := by
@@ -160,7 +160,7 @@ namespace Bundle
 variable {IB}
 
 /-- Characterization of C^n functions into a smooth vector bundle. -/
-theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀ : M} :
+theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace F E) {s : Set M} {x₀ : M} :
     ContMDiffWithinAt IM (IB.prod 𝓘(𝕜, F)) n f s x₀ ↔
       ContMDiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
       ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun x ↦ (trivializationAt F E (f x₀).proj (f x)).2) s x₀ := by
@@ -182,7 +182,7 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀
 #align bundle.cont_mdiff_within_at_total_space Bundle.contMDiffWithinAt_totalSpace
 
 /-- Characterization of C^n functions into a smooth vector bundle. -/
-theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
+theorem contMDiffAt_totalSpace (f : M → TotalSpace F E) (x₀ : M) :
     ContMDiffAt IM (IB.prod 𝓘(𝕜, F)) n f x₀ ↔
       ContMDiffAt IM IB n (fun x => (f x).proj) x₀ ∧
         ContMDiffAt IM 𝓘(𝕜, F) n (fun x => (trivializationAt F E (f x₀).proj (f x)).2) x₀ := by
@@ -191,53 +191,54 @@ theorem contMDiffAt_totalSpace (f : M → TotalSpace E) (x₀ : M) :
 
 /-- Characterization of C^n sections of a smooth vector bundle. -/
 theorem contMDiffAt_section (s : ∀ x, E x) (x₀ : B) :
-    ContMDiffAt IB (IB.prod 𝓘(𝕜, F)) n (fun x => totalSpaceMk x (s x)) x₀ ↔
-      ContMDiffAt IB 𝓘(𝕜, F) n (fun x ↦ (trivializationAt F E x₀ (totalSpaceMk x (s x))).2) x₀ := by
+    ContMDiffAt IB (IB.prod 𝓘(𝕜, F)) n (fun x => TotalSpace.mk' F x (s x)) x₀ ↔
+      ContMDiffAt IB 𝓘(𝕜, F) n (fun x ↦ (trivializationAt F E x₀ ⟨x, s x⟩).2) x₀ := by
   simp_rw [contMDiffAt_totalSpace, and_iff_right_iff_imp]; intro; exact contMDiffAt_id
 #align bundle.cont_mdiff_at_section Bundle.contMDiffAt_section
 
 variable (E)
 
-theorem contMDiff_proj : ContMDiff (IB.prod 𝓘(𝕜, F)) IB n (π E) := fun x ↦ by
+theorem contMDiff_proj : ContMDiff (IB.prod 𝓘(𝕜, F)) IB n (π F E) := fun x ↦ by
   have : ContMDiffAt (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) n id x := contMDiffAt_id
   rw [contMDiffAt_totalSpace] at this
   exact this.1
 #align bundle.cont_mdiff_proj Bundle.contMDiff_proj
 
-theorem smooth_proj : Smooth (IB.prod 𝓘(𝕜, F)) IB (π E) :=
+theorem smooth_proj : Smooth (IB.prod 𝓘(𝕜, F)) IB (π F E) :=
   contMDiff_proj E
 #align bundle.smooth_proj Bundle.smooth_proj
 
-theorem contMDiffOn_proj {s : Set (TotalSpace E)} : ContMDiffOn (IB.prod 𝓘(𝕜, F)) IB n (π E) s :=
+theorem contMDiffOn_proj {s : Set (TotalSpace F E)} :
+    ContMDiffOn (IB.prod 𝓘(𝕜, F)) IB n (π F E) s :=
   (Bundle.contMDiff_proj E).contMDiffOn
 #align bundle.cont_mdiff_on_proj Bundle.contMDiffOn_proj
 
-theorem smoothOn_proj {s : Set (TotalSpace E)} : SmoothOn (IB.prod 𝓘(𝕜, F)) IB (π E) s :=
+theorem smoothOn_proj {s : Set (TotalSpace F E)} : SmoothOn (IB.prod 𝓘(𝕜, F)) IB (π F E) s :=
   contMDiffOn_proj E
 #align bundle.smooth_on_proj Bundle.smoothOn_proj
 
-theorem contMDiffAt_proj {p : TotalSpace E} : ContMDiffAt (IB.prod 𝓘(𝕜, F)) IB n (π E) p :=
+theorem contMDiffAt_proj {p : TotalSpace F E} : ContMDiffAt (IB.prod 𝓘(𝕜, F)) IB n (π F E) p :=
   (Bundle.contMDiff_proj E).contMDiffAt
 #align bundle.cont_mdiff_at_proj Bundle.contMDiffAt_proj
 
-theorem smoothAt_proj {p : TotalSpace E} : SmoothAt (IB.prod 𝓘(𝕜, F)) IB (π E) p :=
+theorem smoothAt_proj {p : TotalSpace F E} : SmoothAt (IB.prod 𝓘(𝕜, F)) IB (π F E) p :=
   Bundle.contMDiffAt_proj E
 #align bundle.smooth_at_proj Bundle.smoothAt_proj
 
-theorem contMDiffWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
-    ContMDiffWithinAt (IB.prod 𝓘(𝕜, F)) IB n (π E) s p :=
+theorem contMDiffWithinAt_proj {s : Set (TotalSpace F E)} {p : TotalSpace F E} :
+    ContMDiffWithinAt (IB.prod 𝓘(𝕜, F)) IB n (π F E) s p :=
   (Bundle.contMDiffAt_proj E).contMDiffWithinAt
 #align bundle.cont_mdiff_within_at_proj Bundle.contMDiffWithinAt_proj
 
-theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
-    SmoothWithinAt (IB.prod 𝓘(𝕜, F)) IB (π E) s p :=
+theorem smoothWithinAt_proj {s : Set (TotalSpace F E)} {p : TotalSpace F E} :
+    SmoothWithinAt (IB.prod 𝓘(𝕜, F)) IB (π F E) s p :=
   Bundle.contMDiffWithinAt_proj E
 #align bundle.smooth_within_at_proj Bundle.smoothWithinAt_proj
 
 variable (𝕜) [∀ x, AddCommMonoid (E x)]
 variable [∀ x, Module 𝕜 (E x)] [VectorBundle 𝕜 F E]
 
-theorem smooth_zeroSection : Smooth IB (IB.prod 𝓘(𝕜, F)) (zeroSection E) := fun x ↦ by
+theorem smooth_zeroSection : Smooth IB (IB.prod 𝓘(𝕜, F)) (zeroSection F E) := fun x ↦ by
   unfold zeroSection
   rw [Bundle.contMDiffAt_section]
   apply (contMDiffAt_const (c := 0)).congr_of_eventuallyEq
@@ -262,7 +263,7 @@ variable [NontriviallyNormedField 𝕜] {EB : Type _} [NormedAddCommGroup EB] [N
 
 section WithTopology
 
-variable [TopologicalSpace (TotalSpace E)] [∀ x, TopologicalSpace (E x)] (F E)
+variable [TopologicalSpace (TotalSpace F E)] [∀ x, TopologicalSpace (E x)] (F E)
 
 variable [FiberBundle F E] [VectorBundle 𝕜 F E]
 
@@ -272,7 +273,7 @@ registers that the bundle is smooth, in the sense of having smooth transition fu
 This is a mixin, not carrying any new data. -/
 class SmoothVectorBundle : Prop where
   protected smoothOn_coordChangeL :
-    ∀ (e e' : Trivialization F (π E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e'],
+    ∀ (e e' : Trivialization F (π F E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e'],
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
         (e.baseSet ∩ e'.baseSet)
 #align smooth_vector_bundle SmoothVectorBundle
@@ -283,7 +284,7 @@ variable [SmoothVectorBundle F E IB]
 section SmoothCoordChange
 
 variable {F E}
-variable (e e' : Trivialization F (π E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e']
+variable (e e' : Trivialization F (π F E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e']
 
 theorem smoothOn_coordChangeL :
     SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
@@ -427,8 +428,8 @@ theorem Trivialization.contMDiffOn_symm_trans :
 
 variable {IB e e'}
 
-theorem ContMDiffWithinAt.change_section_trivialization {f : M → TotalSpace E}
-    (hp : ContMDiffWithinAt IM IB n (π E ∘ f) s x)
+theorem ContMDiffWithinAt.change_section_trivialization {f : M → TotalSpace F E}
+    (hp : ContMDiffWithinAt IM IB n (π F E ∘ f) s x)
     (hf : ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e (f y)).2) s x)
     (he : f x ∈ e.source) (he' : f x ∈ e'.source) :
     ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e' (f y)).2) s x := by
@@ -438,8 +439,8 @@ theorem ContMDiffWithinAt.change_section_trivialization {f : M → TotalSpace E}
     rw [Function.comp_apply, e.coordChange_apply_snd _ hy]
   · rw [Function.comp_apply, e.coordChange_apply_snd _ he]
 
-theorem Trivialization.contMDiffWithinAt_snd_comp_iff₂ {f : M → TotalSpace E}
-    (hp : ContMDiffWithinAt IM IB n (π E ∘ f) s x)
+theorem Trivialization.contMDiffWithinAt_snd_comp_iff₂ {f : M → TotalSpace F E}
+    (hp : ContMDiffWithinAt IM IB n (π F E ∘ f) s x)
     (he : f x ∈ e.source) (he' : f x ∈ e'.source) :
     ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e (f y)).2) s x ↔
       ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e' (f y)).2) s x :=
@@ -451,7 +452,7 @@ end SmoothCoordChange
 between two trivializations `e`, `e'` for `E`, considered as charts to `B × F`, is smooth and
 fiberwise linear. -/
 instance SmoothFiberwiseLinear.hasGroupoid :
-    HasGroupoid (TotalSpace E) (smoothFiberwiseLinear B F IB) where
+    HasGroupoid (TotalSpace F E) (smoothFiberwiseLinear B F IB) where
   compatible := by
     rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩
     haveI : MemTrivializationAtlas e := ⟨he⟩
@@ -468,7 +469,7 @@ instance SmoothFiberwiseLinear.hasGroupoid :
 
 /-- A smooth vector bundle `E` is naturally a smooth manifold. -/
 instance Bundle.TotalSpace.smoothManifoldWithCorners :
-    SmoothManifoldWithCorners (IB.prod 𝓘(𝕜, F)) (TotalSpace E) := by
+    SmoothManifoldWithCorners (IB.prod 𝓘(𝕜, F)) (TotalSpace F E) := by
   refine' { StructureGroupoid.HasGroupoid.comp (smoothFiberwiseLinear B F IB) _ with }
   intro e he
   rw [mem_smoothFiberwiseLinear_iff] at he
@@ -487,9 +488,9 @@ instance Bundle.TotalSpace.smoothManifoldWithCorners :
 section
 
 variable {F E}
-variable {e e' : Trivialization F (π E)} [MemTrivializationAtlas e] [MemTrivializationAtlas e']
+variable {e e' : Trivialization F (π F E)} [MemTrivializationAtlas e] [MemTrivializationAtlas e']
 
-theorem Trivialization.contMDiffWithinAt_iff {f : M → TotalSpace E} {s : Set M} {x₀ : M}
+theorem Trivialization.contMDiffWithinAt_iff {f : M → TotalSpace F E} {s : Set M} {x₀ : M}
     (he : f x₀ ∈ e.source) :
     ContMDiffWithinAt IM (IB.prod 𝓘(𝕜, F)) n f s x₀ ↔
       ContMDiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
@@ -497,13 +498,13 @@ theorem Trivialization.contMDiffWithinAt_iff {f : M → TotalSpace E} {s : Set M
   (contMDiffWithinAt_totalSpace _).trans <| and_congr_right fun h ↦
     Trivialization.contMDiffWithinAt_snd_comp_iff₂ h FiberBundle.mem_trivializationAt_proj_source he
 
-theorem Trivialization.contMDiffAt_iff {f : M → TotalSpace E} {x₀ : M} (he : f x₀ ∈ e.source) :
+theorem Trivialization.contMDiffAt_iff {f : M → TotalSpace F E} {x₀ : M} (he : f x₀ ∈ e.source) :
     ContMDiffAt IM (IB.prod 𝓘(𝕜, F)) n f x₀ ↔
       ContMDiffAt IM IB n (fun x => (f x).proj) x₀ ∧
       ContMDiffAt IM 𝓘(𝕜, F) n (fun x ↦ (e (f x)).2) x₀ :=
   e.contMDiffWithinAt_iff _ he
 
-theorem Trivialization.contMDiffOn_iff {f : M → TotalSpace E} {s : Set M}
+theorem Trivialization.contMDiffOn_iff {f : M → TotalSpace F E} {s : Set M}
     (he : MapsTo f s e.source) :
     ContMDiffOn IM (IB.prod 𝓘(𝕜, F)) n f s ↔
       ContMDiffOn IM IB n (fun x => (f x).proj) s ∧
@@ -511,42 +512,42 @@ theorem Trivialization.contMDiffOn_iff {f : M → TotalSpace E} {s : Set M}
   simp only [ContMDiffOn, ← forall_and]
   exact forall₂_congr fun x hx ↦ e.contMDiffWithinAt_iff IB (he hx)
 
-theorem Trivialization.contMDiff_iff {f : M → TotalSpace E} (he : ∀ x, f x ∈ e.source) :
+theorem Trivialization.contMDiff_iff {f : M → TotalSpace F E} (he : ∀ x, f x ∈ e.source) :
     ContMDiff IM (IB.prod 𝓘(𝕜, F)) n f ↔
       ContMDiff IM IB n (fun x => (f x).proj) ∧
       ContMDiff IM 𝓘(𝕜, F) n (fun x ↦ (e (f x)).2) :=
   (forall_congr' fun x ↦ e.contMDiffAt_iff IB (he x)).trans forall_and
 
-theorem Trivialization.smoothWithinAt_iff {f : M → TotalSpace E} {s : Set M} {x₀ : M}
+theorem Trivialization.smoothWithinAt_iff {f : M → TotalSpace F E} {s : Set M} {x₀ : M}
     (he : f x₀ ∈ e.source) :
     SmoothWithinAt IM (IB.prod 𝓘(𝕜, F)) f s x₀ ↔
       SmoothWithinAt IM IB (fun x => (f x).proj) s x₀ ∧
       SmoothWithinAt IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) s x₀ :=
   e.contMDiffWithinAt_iff IB he
 
-theorem Trivialization.smoothAt_iff {f : M → TotalSpace E} {x₀ : M} (he : f x₀ ∈ e.source) :
+theorem Trivialization.smoothAt_iff {f : M → TotalSpace F E} {x₀ : M} (he : f x₀ ∈ e.source) :
     SmoothAt IM (IB.prod 𝓘(𝕜, F)) f x₀ ↔
       SmoothAt IM IB (fun x => (f x).proj) x₀ ∧ SmoothAt IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) x₀ :=
   e.contMDiffAt_iff IB he
 
-theorem Trivialization.smoothOn_iff {f : M → TotalSpace E} {s : Set M}
+theorem Trivialization.smoothOn_iff {f : M → TotalSpace F E} {s : Set M}
     (he : MapsTo f s e.source) :
     SmoothOn IM (IB.prod 𝓘(𝕜, F)) f s ↔
       SmoothOn IM IB (fun x => (f x).proj) s ∧ SmoothOn IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) s :=
   e.contMDiffOn_iff IB he
 
-theorem Trivialization.smooth_iff {f : M → TotalSpace E} (he : ∀ x, f x ∈ e.source) :
+theorem Trivialization.smooth_iff {f : M → TotalSpace F E} (he : ∀ x, f x ∈ e.source) :
     Smooth IM (IB.prod 𝓘(𝕜, F)) f ↔
       Smooth IM IB (fun x => (f x).proj) ∧ Smooth IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) :=
   e.contMDiff_iff IB he
 
-theorem Trivialization.smoothOn (e : Trivialization F (π E)) [MemTrivializationAtlas e] :
+theorem Trivialization.smoothOn (e : Trivialization F (π F E)) [MemTrivializationAtlas e] :
     SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) e e.source := by
   have : SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) id e.source := smoothOn_id
   rw [e.smoothOn_iff IB (mapsTo_id _)] at this
   exact (this.1.prod_mk this.2).congr fun x hx ↦ (e.mk_proj_snd hx).symm
 
-theorem Trivialization.smoothOn_symm (e : Trivialization F (π E)) [MemTrivializationAtlas e] :
+theorem Trivialization.smoothOn_symm (e : Trivialization F (π F E)) [MemTrivializationAtlas e] :
     SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) e.toLocalHomeomorph.symm e.target := by
   rw [e.smoothOn_iff IB e.toLocalHomeomorph.symm_mapsTo]
   refine ⟨smoothOn_fst.congr fun x hx ↦ e.proj_symm_apply hx, smoothOn_snd.congr fun x hx ↦ ?_⟩
@@ -605,10 +606,10 @@ instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivia
 section Prod
 
 variable (F₁ : Type _) [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _)
-  [TopologicalSpace (TotalSpace E₁)] [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
+  [TopologicalSpace (TotalSpace F₁ E₁)] [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
 
 variable (F₂ : Type _) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type _)
-  [TopologicalSpace (TotalSpace E₂)] [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)]
+  [TopologicalSpace (TotalSpace F₂ E₂)] [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)]
 
 variable [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)] [FiberBundle F₁ E₁]
   [FiberBundle F₂ E₂] [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] [SmoothVectorBundle F₁ E₁ IB]
@@ -646,10 +647,10 @@ class IsSmooth (a : VectorPrebundle 𝕜 F E) : Prop where
       ∃ f : B → F →L[𝕜] F,
         SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) f (e.baseSet ∩ e'.baseSet) ∧
           ∀ (b : B) (_ : b ∈ e.baseSet ∩ e'.baseSet) (v : F),
-            f b v = (e' (totalSpaceMk b (e.symm b v))).2
+            f b v = (e' ⟨b, e.symm b v⟩).2
 #align vector_prebundle.is_smooth VectorPrebundle.IsSmooth
 
-variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π E)}
+variable (a : VectorPrebundle 𝕜 F E) [ha : a.IsSmooth IB] {e e' : Pretrivialization F (π F E)}
 
 /-- A randomly chosen coordinate change on a `SmoothVectorPrebundle`, given by
   the field `exists_coordChange`. Note that `a.smoothCoordChange` need not be the same as
@@ -669,13 +670,13 @@ theorem smoothOn_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
 
 theorem smoothCoordChange_apply (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
-    a.smoothCoordChange IB he he' b v = (e' (totalSpaceMk b (e.symm b v))).2 :=
+    a.smoothCoordChange IB he he' b v = (e' ⟨b, e.symm b v⟩).2 :=
   (Classical.choose_spec (ha.exists_smoothCoordChange e he e' he')).2 b hb v
 #align vector_prebundle.smooth_coord_change_apply VectorPrebundle.smoothCoordChange_apply
 
 theorem mk_smoothCoordChange (he : e ∈ a.pretrivializationAtlas)
     (he' : e' ∈ a.pretrivializationAtlas) {b : B} (hb : b ∈ e.baseSet ∩ e'.baseSet) (v : F) :
-    (b, a.smoothCoordChange IB he he' b v) = e' (totalSpaceMk b (e.symm b v)) := by
+    (b, a.smoothCoordChange IB he he' b v) = e' ⟨b, e.symm b v⟩ := by
   ext
   · rw [e.mk_symm hb.1 v, e'.coe_fst', e.proj_symm_apply' hb.1]
     rw [e.proj_symm_apply' hb.1]; exact hb.2

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -422,7 +422,7 @@ theorem Trivialization.contMDiffOn_symm_trans :
   rintro ⟨b, x⟩ hb
   refine Prod.ext ?_ rfl
   · have : (e.toLocalHomeomorph.symm (b, x)).1 ∈ e'.baseSet
-    . simp_all only [Trivialization.mem_target, mfld_simps]
+    · simp_all only [Trivialization.mem_target, mfld_simps]
     exact (e'.coe_fst' this).trans (e.proj_symm_apply hb.1)
 
 variable {IB e e'}

Add lemmas about smoothness in a smooth vector bundle. Also rename the old smoothOn_coordChange to smoothOn_coordChangeL.

@@ -170,14 +170,11 @@ theorem contMDiffWithinAt_totalSpace (f : M → TotalSpace E) {s : Set M} {x₀
   simp_rw [modelWithCornersSelf_prod, FiberBundle.extChartAt, Function.comp, LocalEquiv.trans_apply,
     LocalEquiv.prod_coe, LocalEquiv.refl_coe, extChartAt_self_apply, modelWithCornersSelf_coe,
     id_def]
-  refine' (contMDiffWithinAt_prod_iff _).trans _
-  -- rw doesn't do this?
+  refine (contMDiffWithinAt_prod_iff _).trans (and_congr ?_ Iff.rfl)
   have h1 : (fun x => (f x).proj) ⁻¹' (trivializationAt F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
-    ((FiberBundle.continuous_proj F E).continuousWithinAt.comp hf
-        (mapsTo_image f s)).preimage_mem_nhdsWithin
+    ((FiberBundle.continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s))
       ((Trivialization.open_baseSet _).mem_nhds (mem_baseSet_trivializationAt F E _))
-  refine'
-    and_congr (EventuallyEq.contMDiffWithinAt_iff (eventually_of_mem h1 fun x hx => _) _) Iff.rfl
+  refine EventuallyEq.contMDiffWithinAt_iff (eventually_of_mem h1 fun x hx => ?_) ?_
   · simp_rw [Function.comp, LocalHomeomorph.coe_coe, Trivialization.coe_coe]
     rw [Trivialization.coe_fst']
     exact hx
@@ -201,18 +198,10 @@ theorem contMDiffAt_section (s : ∀ x, E x) (x₀ : B) :
 
 variable (E)
 
-theorem contMDiff_proj : ContMDiff (IB.prod 𝓘(𝕜, F)) IB n (π E) := by
-  intro x
-  rw [ContMDiffAt, contMDiffWithinAt_iff']
-  refine' ⟨(FiberBundle.continuous_proj F E).continuousWithinAt, _⟩
-  simp_rw [(· ∘ ·), FiberBundle.extChartAt]
-  apply contDiffWithinAt_fst.congr
-  · rintro ⟨a, b⟩ hab
-    simp only [mfld_simps] at hab
-    have : ((chartAt HB x.1).symm (IB.symm a), b) ∈ (trivializationAt F E x.fst).target := by
-      simp only [hab, mfld_simps]
-    simp only [Trivialization.proj_symm_apply _ this, hab, mfld_simps]
-  · simp only [mfld_simps]
+theorem contMDiff_proj : ContMDiff (IB.prod 𝓘(𝕜, F)) IB n (π E) := fun x ↦ by
+  have : ContMDiffAt (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) n id x := contMDiffAt_id
+  rw [contMDiffAt_totalSpace] at this
+  exact this.1
 #align bundle.cont_mdiff_proj Bundle.contMDiff_proj
 
 theorem smooth_proj : Smooth (IB.prod 𝓘(𝕜, F)) IB (π E) :=
@@ -248,16 +237,13 @@ theorem smoothWithinAt_proj {s : Set (TotalSpace E)} {p : TotalSpace E} :
 variable (𝕜) [∀ x, AddCommMonoid (E x)]
 variable [∀ x, Module 𝕜 (E x)] [VectorBundle 𝕜 F E]
 
-theorem smooth_zeroSection : Smooth IB (IB.prod 𝓘(𝕜, F)) (zeroSection E) := by
-  intro x
-  rw [Bundle.contMDiffAt_totalSpace]
-  refine' ⟨contMDiffAt_id, contMDiffAt_const.congr_of_eventuallyEq _⟩
-  · exact 0
-  refine'
-    eventually_of_mem
-      ((trivializationAt F E x).open_baseSet.mem_nhds (mem_baseSet_trivializationAt F E x))
-      fun x' hx' => _
-  simp_rw [zeroSection_proj, (trivializationAt F E x).zeroSection 𝕜 hx']
+theorem smooth_zeroSection : Smooth IB (IB.prod 𝓘(𝕜, F)) (zeroSection E) := fun x ↦ by
+  unfold zeroSection
+  rw [Bundle.contMDiffAt_section]
+  apply (contMDiffAt_const (c := 0)).congr_of_eventuallyEq
+  filter_upwards [(trivializationAt F E x).open_baseSet.mem_nhds
+    (mem_baseSet_trivializationAt F E x)] with y hy
+    using congr_arg Prod.snd <| (trivializationAt F E x).zeroSection 𝕜 hy
 #align bundle.smooth_zero_section Bundle.smooth_zeroSection
 
 end Bundle
@@ -285,16 +271,182 @@ topological vector bundle over `B` with fibers isomorphic to `F`, then `SmoothVe
 registers that the bundle is smooth, in the sense of having smooth transition functions.
 This is a mixin, not carrying any new data. -/
 class SmoothVectorBundle : Prop where
-  smoothOn_coordChange :
+  protected smoothOn_coordChangeL :
     ∀ (e e' : Trivialization F (π E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e'],
       SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
         (e.baseSet ∩ e'.baseSet)
 #align smooth_vector_bundle SmoothVectorBundle
-
-export SmoothVectorBundle (smoothOn_coordChange)
+#align smooth_vector_bundle.smooth_on_coord_change SmoothVectorBundle.smoothOn_coordChangeL
 
 variable [SmoothVectorBundle F E IB]
 
+section SmoothCoordChange
+
+variable {F E}
+variable (e e' : Trivialization F (π E)) [MemTrivializationAtlas e] [MemTrivializationAtlas e']
+
+theorem smoothOn_coordChangeL :
+    SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
+      (e.baseSet ∩ e'.baseSet) :=
+  SmoothVectorBundle.smoothOn_coordChangeL e e'
+
+theorem smoothOn_symm_coordChangeL :
+    SmoothOn IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => ((e.coordChangeL 𝕜 e' b).symm : F →L[𝕜] F))
+      (e.baseSet ∩ e'.baseSet) := by
+  rw [inter_comm]
+  refine (SmoothVectorBundle.smoothOn_coordChangeL e' e).congr fun b hb ↦ ?_
+  rw [e.symm_coordChangeL e' hb]
+
+theorem contMDiffOn_coordChangeL :
+    ContMDiffOn IB 𝓘(𝕜, F →L[𝕜] F) n (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F))
+      (e.baseSet ∩ e'.baseSet) :=
+  (smoothOn_coordChangeL IB e e').of_le le_top
+
+theorem contMDiffOn_symm_coordChangeL :
+    ContMDiffOn IB 𝓘(𝕜, F →L[𝕜] F) n (fun b : B => ((e.coordChangeL 𝕜 e' b).symm : F →L[𝕜] F))
+      (e.baseSet ∩ e'.baseSet) :=
+  (smoothOn_symm_coordChangeL IB e e').of_le le_top
+
+variable {e e'}
+
+theorem contMDiffAt_coordChangeL (h : x ∈ e.baseSet) (h' : x ∈ e'.baseSet) :
+    ContMDiffAt IB 𝓘(𝕜, F →L[𝕜] F) n (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F)) x :=
+  (contMDiffOn_coordChangeL IB e e').contMDiffAt <|
+    (e.open_baseSet.inter e'.open_baseSet).mem_nhds ⟨h, h'⟩
+
+theorem smoothAt_coordChangeL (h : x ∈ e.baseSet) (h' : x ∈ e'.baseSet) :
+    SmoothAt IB 𝓘(𝕜, F →L[𝕜] F) (fun b : B => (e.coordChangeL 𝕜 e' b : F →L[𝕜] F)) x :=
+  contMDiffAt_coordChangeL IB h h'
+
+variable {IB}
+
+protected theorem ContMDiffWithinAt.coordChangeL {f : M → B}
+    (hf : ContMDiffWithinAt IM IB n f s x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    ContMDiffWithinAt IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s x :=
+  (contMDiffAt_coordChangeL IB he he').comp_contMDiffWithinAt _ hf
+
+protected nonrec theorem ContMDiffAt.coordChangeL {f : M → B}
+    (hf : ContMDiffAt IM IB n f x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    ContMDiffAt IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) x :=
+  hf.coordChangeL he he'
+
+protected theorem ContMDiffOn.coordChangeL {f : M → B}
+    (hf : ContMDiffOn IM IB n f s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
+    ContMDiffOn IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s :=
+  fun x hx ↦ (hf x hx).coordChangeL (he hx) (he' hx)
+
+protected theorem ContMDiff.coordChangeL {f : M → B}
+    (hf : ContMDiff IM IB n f) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
+    ContMDiff IM 𝓘(𝕜, F →L[𝕜] F) n (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) := fun x ↦
+  (hf x).coordChangeL (he x) (he' x)
+
+protected nonrec theorem SmoothWithinAt.coordChangeL {f : M → B}
+    (hf : SmoothWithinAt IM IB f s x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    SmoothWithinAt IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s x :=
+  hf.coordChangeL he he'
+
+protected nonrec theorem SmoothAt.coordChangeL {f : M → B}
+    (hf : SmoothAt IM IB f x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    SmoothAt IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) x :=
+  hf.coordChangeL he he'
+
+protected nonrec theorem SmoothOn.coordChangeL {f : M → B}
+    (hf : SmoothOn IM IB f s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
+    SmoothOn IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) s :=
+  hf.coordChangeL he he'
+
+protected nonrec theorem Smooth.coordChangeL {f : M → B}
+    (hf : Smooth IM IB f) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
+    Smooth IM 𝓘(𝕜, F →L[𝕜] F) (fun y ↦ (e.coordChangeL 𝕜 e' (f y) : F →L[𝕜] F)) :=
+  hf.coordChangeL he he'
+
+protected theorem ContMDiffWithinAt.coordChange {f : M → B} {g : M → F}
+    (hf : ContMDiffWithinAt IM IB n f s x) (hg : ContMDiffWithinAt IM 𝓘(𝕜, F) n g s x)
+    (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) s x := by
+  refine ((hf.coordChangeL he he').clm_apply hg).congr_of_eventuallyEq ?_ ?_
+  · have : e.baseSet ∩ e'.baseSet ∈ 𝓝 (f x) :=
+     (e.open_baseSet.inter e'.open_baseSet).mem_nhds ⟨he, he'⟩
+    filter_upwards [hf.continuousWithinAt this] with y hy
+    exact (Trivialization.coordChangeL_apply' e e' hy (g y)).symm
+  · exact (Trivialization.coordChangeL_apply' e e' ⟨he, he'⟩ (g x)).symm
+
+protected nonrec theorem ContMDiffAt.coordChange {f : M → B} {g : M → F}
+    (hf : ContMDiffAt IM IB n f x) (hg : ContMDiffAt IM 𝓘(𝕜, F) n g x) (he : f x ∈ e.baseSet)
+    (he' : f x ∈ e'.baseSet) :
+    ContMDiffAt IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) x :=
+  hf.coordChange hg he he'
+
+protected theorem ContMDiffOn.coordChange {f : M → B} {g : M → F} (hf : ContMDiffOn IM IB n f s)
+    (hg : ContMDiffOn IM 𝓘(𝕜, F) n g s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
+    ContMDiffOn IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) s := fun x hx ↦
+  (hf x hx).coordChange (hg x hx) (he hx) (he' hx)
+
+protected theorem ContMDiff.coordChange {f : M → B} {g : M → F} (hf : ContMDiff IM IB n f)
+    (hg : ContMDiff IM 𝓘(𝕜, F) n g) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
+    ContMDiff IM 𝓘(𝕜, F) n (fun y ↦ e.coordChange e' (f y) (g y)) := fun x ↦
+  (hf x).coordChange (hg x) (he x) (he' x)
+
+protected nonrec theorem SmoothWithinAt.coordChange {f : M → B} {g : M → F}
+    (hf : SmoothWithinAt IM IB f s x) (hg : SmoothWithinAt IM 𝓘(𝕜, F) g s x)
+    (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    SmoothWithinAt IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) s x :=
+  hf.coordChange hg he he'
+
+protected nonrec theorem SmoothAt.coordChange {f : M → B} {g : M → F} (hf : SmoothAt IM IB f x)
+    (hg : SmoothAt IM 𝓘(𝕜, F) g x) (he : f x ∈ e.baseSet) (he' : f x ∈ e'.baseSet) :
+    SmoothAt IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) x :=
+  hf.coordChange hg he he'
+
+protected nonrec theorem SmoothOn.coordChange {f : M → B} {g : M → F} (hf : SmoothOn IM IB f s)
+    (hg : SmoothOn IM 𝓘(𝕜, F) g s) (he : MapsTo f s e.baseSet) (he' : MapsTo f s e'.baseSet) :
+    SmoothOn IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) s :=
+  hf.coordChange hg he he'
+
+protected theorem Smooth.coordChange {f : M → B} {g : M → F} (hf : Smooth IM IB f)
+    (hg : Smooth IM 𝓘(𝕜, F) g) (he : ∀ x, f x ∈ e.baseSet) (he' : ∀ x, f x ∈ e'.baseSet) :
+    Smooth IM 𝓘(𝕜, F) (fun y ↦ e.coordChange e' (f y) (g y)) := fun x ↦
+  (hf x).coordChange (hg x) (he x) (he' x)
+
+variable (IB e e')
+
+theorem Trivialization.contMDiffOn_symm_trans :
+    ContMDiffOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) n
+      (e.toLocalHomeomorph.symm ≫ₕ e'.toLocalHomeomorph) (e.target ∩ e'.target) := by
+  have Hmaps : MapsTo Prod.fst (e.target ∩ e'.target) (e.baseSet ∩ e'.baseSet) := fun x hx ↦
+    ⟨e.mem_target.1 hx.1, e'.mem_target.1 hx.2⟩
+  rw [mapsTo_inter] at Hmaps
+  -- TODO: drop `congr` #5473
+  refine (contMDiffOn_fst.prod_mk
+    (contMDiffOn_fst.coordChange contMDiffOn_snd Hmaps.1 Hmaps.2)).congr ?_
+  rintro ⟨b, x⟩ hb
+  refine Prod.ext ?_ rfl
+  · have : (e.toLocalHomeomorph.symm (b, x)).1 ∈ e'.baseSet
+    . simp_all only [Trivialization.mem_target, mfld_simps]
+    exact (e'.coe_fst' this).trans (e.proj_symm_apply hb.1)
+
+variable {IB e e'}
+
+theorem ContMDiffWithinAt.change_section_trivialization {f : M → TotalSpace E}
+    (hp : ContMDiffWithinAt IM IB n (π E ∘ f) s x)
+    (hf : ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e (f y)).2) s x)
+    (he : f x ∈ e.source) (he' : f x ∈ e'.source) :
+    ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e' (f y)).2) s x := by
+  rw [Trivialization.mem_source] at he he'
+  refine (hp.coordChange hf he he').congr_of_eventuallyEq ?_ ?_
+  · filter_upwards [hp.continuousWithinAt (e.open_baseSet.mem_nhds he)] with y hy
+    rw [Function.comp_apply, e.coordChange_apply_snd _ hy]
+  · rw [Function.comp_apply, e.coordChange_apply_snd _ he]
+
+theorem Trivialization.contMDiffWithinAt_snd_comp_iff₂ {f : M → TotalSpace E}
+    (hp : ContMDiffWithinAt IM IB n (π E ∘ f) s x)
+    (he : f x ∈ e.source) (he' : f x ∈ e'.source) :
+    ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e (f y)).2) s x ↔
+      ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun y ↦ (e' (f y)).2) s x :=
+  ⟨(hp.change_section_trivialization · he he'), (hp.change_section_trivialization · he' he)⟩
+
+end SmoothCoordChange
+
 /-- For a smooth vector bundle `E` over `B` with fiber modelled on `F`, the change-of-co-ordinates
 between two trivializations `e`, `e'` for `E`, considered as charts to `B × F`, is smooth and
 fiberwise linear. -/
@@ -305,18 +457,13 @@ instance SmoothFiberwiseLinear.hasGroupoid :
     haveI : MemTrivializationAtlas e := ⟨he⟩
     haveI : MemTrivializationAtlas e' := ⟨he'⟩
     rw [mem_smoothFiberwiseLinear_iff]
-    refine' ⟨_, _, e.open_baseSet.inter e'.open_baseSet, smoothOn_coordChange e e', _, _, _⟩
-    · rw [inter_comm]
-      apply ContMDiffOn.congr (smoothOn_coordChange e' e)
-      · intro b hb
-        rw [e.symm_coordChangeL e' hb]
+    refine' ⟨_, _, e.open_baseSet.inter e'.open_baseSet, smoothOn_coordChangeL IB e e',
+      smoothOn_symm_coordChangeL IB e e', _⟩
+    refine LocalHomeomorph.eqOnSourceSetoid.symm ⟨?_, ?_⟩
     · simp only [e.symm_trans_source_eq e', FiberwiseLinear.localHomeomorph, trans_toLocalEquiv,
         symm_toLocalEquiv]
     · rintro ⟨b, v⟩ hb
-      have hb' : b ∈ e.baseSet ∩ e'.baseSet := by
-        simpa only [trans_toLocalEquiv, symm_toLocalEquiv, e.symm_trans_source_eq e',
-          coe_coe_symm, prod_mk_mem_set_prod_eq, mem_univ, and_true_iff] using hb
-      exact e.apply_symm_apply_eq_coordChangeL e' hb' v
+      exact (e.apply_symm_apply_eq_coordChangeL e' hb.1 v).symm
 #align smooth_fiberwise_linear.has_groupoid SmoothFiberwiseLinear.hasGroupoid
 
 /-- A smooth vector bundle `E` is naturally a smooth manifold. -/
@@ -337,8 +484,77 @@ instance Bundle.TotalSpace.smoothManifoldWithCorners :
     exact (h2φ.comp contMDiffOn_fst <| prod_subset_preimage_fst _ _).clm_apply contMDiffOn_snd
 #align bundle.total_space.smooth_manifold_with_corners Bundle.TotalSpace.smoothManifoldWithCorners
 
-/-! ### Core construction for smooth vector bundles -/
+section
+
+variable {F E}
+variable {e e' : Trivialization F (π E)} [MemTrivializationAtlas e] [MemTrivializationAtlas e']
+
+theorem Trivialization.contMDiffWithinAt_iff {f : M → TotalSpace E} {s : Set M} {x₀ : M}
+    (he : f x₀ ∈ e.source) :
+    ContMDiffWithinAt IM (IB.prod 𝓘(𝕜, F)) n f s x₀ ↔
+      ContMDiffWithinAt IM IB n (fun x => (f x).proj) s x₀ ∧
+      ContMDiffWithinAt IM 𝓘(𝕜, F) n (fun x ↦ (e (f x)).2) s x₀ :=
+  (contMDiffWithinAt_totalSpace _).trans <| and_congr_right fun h ↦
+    Trivialization.contMDiffWithinAt_snd_comp_iff₂ h FiberBundle.mem_trivializationAt_proj_source he
 
+theorem Trivialization.contMDiffAt_iff {f : M → TotalSpace E} {x₀ : M} (he : f x₀ ∈ e.source) :
+    ContMDiffAt IM (IB.prod 𝓘(𝕜, F)) n f x₀ ↔
+      ContMDiffAt IM IB n (fun x => (f x).proj) x₀ ∧
+      ContMDiffAt IM 𝓘(𝕜, F) n (fun x ↦ (e (f x)).2) x₀ :=
+  e.contMDiffWithinAt_iff _ he
+
+theorem Trivialization.contMDiffOn_iff {f : M → TotalSpace E} {s : Set M}
+    (he : MapsTo f s e.source) :
+    ContMDiffOn IM (IB.prod 𝓘(𝕜, F)) n f s ↔
+      ContMDiffOn IM IB n (fun x => (f x).proj) s ∧
+      ContMDiffOn IM 𝓘(𝕜, F) n (fun x ↦ (e (f x)).2) s := by
+  simp only [ContMDiffOn, ← forall_and]
+  exact forall₂_congr fun x hx ↦ e.contMDiffWithinAt_iff IB (he hx)
+
+theorem Trivialization.contMDiff_iff {f : M → TotalSpace E} (he : ∀ x, f x ∈ e.source) :
+    ContMDiff IM (IB.prod 𝓘(𝕜, F)) n f ↔
+      ContMDiff IM IB n (fun x => (f x).proj) ∧
+      ContMDiff IM 𝓘(𝕜, F) n (fun x ↦ (e (f x)).2) :=
+  (forall_congr' fun x ↦ e.contMDiffAt_iff IB (he x)).trans forall_and
+
+theorem Trivialization.smoothWithinAt_iff {f : M → TotalSpace E} {s : Set M} {x₀ : M}
+    (he : f x₀ ∈ e.source) :
+    SmoothWithinAt IM (IB.prod 𝓘(𝕜, F)) f s x₀ ↔
+      SmoothWithinAt IM IB (fun x => (f x).proj) s x₀ ∧
+      SmoothWithinAt IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) s x₀ :=
+  e.contMDiffWithinAt_iff IB he
+
+theorem Trivialization.smoothAt_iff {f : M → TotalSpace E} {x₀ : M} (he : f x₀ ∈ e.source) :
+    SmoothAt IM (IB.prod 𝓘(𝕜, F)) f x₀ ↔
+      SmoothAt IM IB (fun x => (f x).proj) x₀ ∧ SmoothAt IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) x₀ :=
+  e.contMDiffAt_iff IB he
+
+theorem Trivialization.smoothOn_iff {f : M → TotalSpace E} {s : Set M}
+    (he : MapsTo f s e.source) :
+    SmoothOn IM (IB.prod 𝓘(𝕜, F)) f s ↔
+      SmoothOn IM IB (fun x => (f x).proj) s ∧ SmoothOn IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) s :=
+  e.contMDiffOn_iff IB he
+
+theorem Trivialization.smooth_iff {f : M → TotalSpace E} (he : ∀ x, f x ∈ e.source) :
+    Smooth IM (IB.prod 𝓘(𝕜, F)) f ↔
+      Smooth IM IB (fun x => (f x).proj) ∧ Smooth IM 𝓘(𝕜, F) (fun x ↦ (e (f x)).2) :=
+  e.contMDiff_iff IB he
+
+theorem Trivialization.smoothOn (e : Trivialization F (π E)) [MemTrivializationAtlas e] :
+    SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) e e.source := by
+  have : SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) id e.source := smoothOn_id
+  rw [e.smoothOn_iff IB (mapsTo_id _)] at this
+  exact (this.1.prod_mk this.2).congr fun x hx ↦ (e.mk_proj_snd hx).symm
+
+theorem Trivialization.smoothOn_symm (e : Trivialization F (π E)) [MemTrivializationAtlas e] :
+    SmoothOn (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) e.toLocalHomeomorph.symm e.target := by
+  rw [e.smoothOn_iff IB e.toLocalHomeomorph.symm_mapsTo]
+  refine ⟨smoothOn_fst.congr fun x hx ↦ e.proj_symm_apply hx, smoothOn_snd.congr fun x hx ↦ ?_⟩
+  rw [e.apply_symm_apply hx]
+
+end
+
+/-! ### Core construction for smooth vector bundles -/
 
 namespace VectorBundleCore
 
@@ -360,7 +576,7 @@ variable [Z.IsSmooth IB]
 /-- If a `VectorBundleCore` has the `IsSmooth` mixin, then the vector bundle constructed from it
 is a smooth vector bundle. -/
 instance smoothVectorBundle : SmoothVectorBundle F Z.Fiber IB where
-  smoothOn_coordChange := by
+  smoothOn_coordChangeL := by
     rintro - - ⟨i, rfl⟩ ⟨i', rfl⟩
     -- Porting note: Originally `Z.smoothOn_coordChange IB i i'`
     refine'
@@ -375,7 +591,7 @@ end VectorBundleCore
 
 /-- A trivial vector bundle over a smooth manifold is a smooth vector bundle. -/
 instance Bundle.Trivial.smoothVectorBundle : SmoothVectorBundle F (Bundle.Trivial B F) IB where
-  smoothOn_coordChange := by
+  smoothOn_coordChangeL := by
     intro e e' he he'
     obtain rfl := Bundle.Trivial.eq_trivialization B F e
     obtain rfl := Bundle.Trivial.eq_trivialization B F e'
@@ -400,15 +616,15 @@ variable [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E
 
 /-- The direct sum of two smooth vector bundles over the same base is a smooth vector bundle. -/
 instance Bundle.Prod.smoothVectorBundle : SmoothVectorBundle (F₁ × F₂) (E₁ ×ᵇ E₂) IB where
-  smoothOn_coordChange := by
+  smoothOn_coordChangeL := by
     rintro _ _ ⟨e₁, e₂, i₁, i₂, rfl⟩ ⟨e₁', e₂', i₁', i₂', rfl⟩
     rw [SmoothOn]
     refine' ContMDiffOn.congr _ (e₁.coordChangeL_prod 𝕜 e₁' e₂ e₂')
     refine' ContMDiffOn.clm_prodMap _ _
-    · refine' (smoothOn_coordChange e₁ e₁').mono _
+    · refine' (smoothOn_coordChangeL IB e₁ e₁').mono _
       simp only [Trivialization.baseSet_prod, mfld_simps]
       mfld_set_tac
-    · refine' (smoothOn_coordChange e₂ e₂').mono _
+    · refine' (smoothOn_coordChangeL IB e₂ e₂').mono _
       simp only [Trivialization.baseSet_prod, mfld_simps]
       mfld_set_tac
 #align bundle.prod.smooth_vector_bundle Bundle.Prod.smoothVectorBundle
@@ -471,7 +687,7 @@ variable (IB)
 theorem smoothVectorBundle : @SmoothVectorBundle
     _ _ F E _ _ _ _ _ _ IB _ _ _ _ _ _ a.totalSpaceTopology _ a.toFiberBundle a.toVectorBundle :=
   letI := a.totalSpaceTopology; letI := a.toFiberBundle; letI := a.toVectorBundle
-  { smoothOn_coordChange := by
+  { smoothOn_coordChangeL := by
       rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩
       refine' (a.smoothOn_smoothCoordChange he he').congr _
       intro b hb

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>