topology.fiber_bundle.trivialization | Mathlib porting status

(last sync)

refactor: redefine bundle.total_space (#19221)

Use a custom structure for bundle.total_space.
- Use bundle.total_space.mk instead of bundle.total_space_mk.
- Use bundle.total_space.to_prod instead of equiv.sigma_equiv_prod.
- Use bundle.total_space.mk' (scoped notation) to specify F.
- Rename bundle.trivial.proj_snd to bundle.total_space.trivial_snd to allow dot notation. Should we just use bundle.total_space.snd since bundle.trivial is now reducible?
Add an unused argument to bundle.total_space.
Make bundle.trivial and bundle.continuous_linear_map reducible.
Drop instances that are no longer needed.

Diff

@@ -159,9 +159,9 @@ lemma symm_trans_target_eq (e e' : pretrivialization F proj) :
   (e.to_local_equiv.symm.trans e'.to_local_equiv).target = (e.base_set ∩ e'.base_set) ×ˢ univ :=
 by rw [← local_equiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
 
-variables {B F} (e' : pretrivialization F (π E)) {x' : total_space E} {b : B} {y : E b}
+variables {B F} (e' : pretrivialization F (π F E)) {x' : total_space F E} {b : B} {y : E b}
 
-lemma coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.base_set := e'.mem_source
+@[simp] theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.base_set := e'.mem_source
 
 @[simp, mfld_simps] lemma coe_coe_fst (hb : b ∈ e'.base_set) : (e' y).1 = b :=
 e'.coe_fst (e'.mem_source.2 hb)
@@ -169,7 +169,7 @@ e'.coe_fst (e'.mem_source.2 hb)
 lemma mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.base_set :=
 e'.mem_target
 
-lemma symm_coe_proj {x : B} {y : F} (e' : pretrivialization F (π E)) (h : x ∈ e'.base_set) :
+lemma symm_coe_proj {x : B} {y : F} (e' : pretrivialization F (π F E)) (h : x ∈ e'.base_set) :
   (e'.to_local_equiv.symm (x, y)).1 = x :=
 e'.proj_symm_apply' h
 
@@ -177,46 +177,46 @@ section has_zero
 variables [∀ x, has_zero (E x)]
 
 /-- A fiberwise inverse to `e`. This is the function `F → E b` that induces a local inverse
-`B × F → total_space E` of `e` on `e.base_set`. It is defined to be `0` outside `e.base_set`. -/
-protected noncomputable def symm (e : pretrivialization F (π E)) (b : B) (y : F) : E b :=
+`B × F → total_space F E` of `e` on `e.base_set`. It is defined to be `0` outside `e.base_set`. -/
+protected noncomputable def symm (e : pretrivialization F (π F E)) (b : B) (y : F) : E b :=
 if hb : b ∈ e.base_set
 then cast (congr_arg E (e.proj_symm_apply' hb)) (e.to_local_equiv.symm (b, y)).2
 else 0
 
-lemma symm_apply (e : pretrivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
+lemma symm_apply (e : pretrivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
   e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.to_local_equiv.symm (b, y)).2 :=
 dif_pos hb
 
-lemma symm_apply_of_not_mem (e : pretrivialization F (π E)) {b : B} (hb : b ∉ e.base_set) (y : F) :
-  e.symm b y = 0 :=
+lemma symm_apply_of_not_mem (e : pretrivialization F (π F E)) {b : B} (hb : b ∉ e.base_set)
+  (y : F) : e.symm b y = 0 :=
 dif_neg hb
 
-lemma coe_symm_of_not_mem (e : pretrivialization F (π E)) {b : B} (hb : b ∉ e.base_set) :
+lemma coe_symm_of_not_mem (e : pretrivialization F (π F E)) {b : B} (hb : b ∉ e.base_set) :
   (e.symm b : F → E b) = 0 :=
 funext $ λ y, dif_neg hb
 
-lemma mk_symm (e : pretrivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
-  total_space_mk b (e.symm b y) = e.to_local_equiv.symm (b, y) :=
+lemma mk_symm (e : pretrivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
+  total_space.mk b (e.symm b y) = e.to_local_equiv.symm (b, y) :=
 by rw [e.symm_apply hb, total_space.mk_cast, total_space.eta]
 
-lemma symm_proj_apply (e : pretrivialization F (π E)) (z : total_space E)
+lemma symm_proj_apply (e : pretrivialization F (π F E)) (z : total_space F E)
   (hz : z.proj ∈ e.base_set) : e.symm z.proj (e z).2 = z.2 :=
 by rw [e.symm_apply hz, cast_eq_iff_heq, e.mk_proj_snd' hz,
   e.symm_apply_apply (e.mem_source.mpr hz)]
 
-lemma symm_apply_apply_mk (e : pretrivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : E b) :
-  e.symm b (e (total_space_mk b y)).2 = y :=
-e.symm_proj_apply (total_space_mk b y) hb
+lemma symm_apply_apply_mk (e : pretrivialization F (π F E)) {b : B} (hb : b ∈ e.base_set)
+  (y : E b) : e.symm b (e ⟨b, y⟩).2 = y :=
+e.symm_proj_apply ⟨b, y⟩ hb
 
-lemma apply_mk_symm (e : pretrivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
-  e (total_space_mk b (e.symm b y)) = (b, y) :=
+lemma apply_mk_symm (e : pretrivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
+  e ⟨b, e.symm b y⟩ = (b, y) :=
 by rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
 
 end has_zero
 
 end pretrivialization
 
-variables [topological_space Z] [topological_space (total_space E)]
+variables [topological_space Z] [topological_space (total_space F E)]
 
 /--
 A structure extending local homeomorphisms, defining a local trivialization of a projection
@@ -403,7 +403,7 @@ begin
   exact hf_proj.preimage_mem_nhds (e.open_base_set.mem_nhds he),
 end
 
-variables {E} (e' : trivialization F (π E)) {x' : total_space E} {b : B} {y : E b}
+variables {E} (e' : trivialization F (π F E)) {x' : total_space F E} {b : B} {y : E b}
 
 protected lemma continuous_on : continuous_on e' e'.source := e'.continuous_to_fun
 
@@ -418,51 +418,52 @@ e'.coe_fst (e'.mem_source.2 hb)
 lemma mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.base_set :=
 e'.to_pretrivialization.mem_target
 
-lemma symm_apply_apply {x : total_space E} (hx : x ∈ e'.source) :
+lemma symm_apply_apply {x : total_space F E} (hx : x ∈ e'.source) :
   e'.to_local_homeomorph.symm (e' x) = x :=
 e'.to_local_equiv.left_inv hx
 
 @[simp, mfld_simps] lemma symm_coe_proj {x : B} {y : F}
-  (e : trivialization F (π E)) (h : x ∈ e.base_set) :
+  (e : trivialization F (π F E)) (h : x ∈ e.base_set) :
   (e.to_local_homeomorph.symm (x, y)).1 = x := e.proj_symm_apply' h
 
 section has_zero
 variables [∀ x, has_zero (E x)]
 
 /-- A fiberwise inverse to `e'`. The function `F → E x` that induces a local inverse
-`B × F → total_space E` of `e'` on `e'.base_set`. It is defined to be `0` outside `e'.base_set`. -/
-protected noncomputable def symm (e : trivialization F (π E)) (b : B) (y : F) : E b :=
+`B × F → total_space F E` of `e'` on `e'.base_set`. It is defined to be `0` outside
+`e'.base_set`. -/
+protected noncomputable def symm (e : trivialization F (π F E)) (b : B) (y : F) : E b :=
 e.to_pretrivialization.symm b y
 
-lemma symm_apply (e : trivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
+lemma symm_apply (e : trivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
   e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.to_local_homeomorph.symm (b, y)).2 :=
 dif_pos hb
 
-lemma symm_apply_of_not_mem (e : trivialization F (π E)) {b : B} (hb : b ∉ e.base_set) (y : F) :
+lemma symm_apply_of_not_mem (e : trivialization F (π F E)) {b : B} (hb : b ∉ e.base_set) (y : F) :
   e.symm b y = 0 :=
 dif_neg hb
 
-lemma mk_symm (e : trivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
-  total_space_mk b (e.symm b y) = e.to_local_homeomorph.symm (b, y) :=
+lemma mk_symm (e : trivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
+  total_space.mk b (e.symm b y) = e.to_local_homeomorph.symm (b, y) :=
 e.to_pretrivialization.mk_symm hb y
 
-lemma symm_proj_apply (e : trivialization F (π E)) (z : total_space E)
+lemma symm_proj_apply (e : trivialization F (π F E)) (z : total_space F E)
   (hz : z.proj ∈ e.base_set) : e.symm z.proj (e z).2 = z.2 :=
 e.to_pretrivialization.symm_proj_apply z hz
 
-lemma symm_apply_apply_mk (e : trivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : E b) :
-  e.symm b (e (total_space_mk b y)).2 = y :=
-e.symm_proj_apply (total_space_mk b y) hb
+lemma symm_apply_apply_mk (e : trivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : E b) :
+  e.symm b (e ⟨b, y⟩).2 = y :=
+e.symm_proj_apply ⟨b, y⟩ hb
 
-lemma apply_mk_symm (e : trivialization F (π E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
-  e (total_space_mk b (e.symm b y)) = (b, y) :=
+lemma apply_mk_symm (e : trivialization F (π F E)) {b : B} (hb : b ∈ e.base_set) (y : F) :
+  e ⟨b, e.symm b y⟩ = (b, y) :=
 e.to_pretrivialization.apply_mk_symm hb y
 
-lemma continuous_on_symm (e : trivialization F (π E)) :
-  continuous_on (λ z : B × F, total_space_mk z.1 (e.symm z.1 z.2)) (e.base_set ×ˢ univ) :=
+lemma continuous_on_symm (e : trivialization F (π F E)) :
+  continuous_on (λ z : B × F, total_space.mk' F z.1 (e.symm z.1 z.2)) (e.base_set ×ˢ univ) :=
 begin
   have : ∀ (z : B × F) (hz : z ∈ e.base_set ×ˢ (univ : set F)),
-    total_space_mk z.1 (e.symm z.1 z.2) = e.to_local_homeomorph.symm z,
+    total_space.mk z.1 (e.symm z.1 z.2) = e.to_local_homeomorph.symm z,
   { rintro x ⟨hx : x.1 ∈ e.base_set, _⟩, simp_rw [e.mk_symm hx, prod.mk.eta] },
   refine continuous_on.congr _ this,
   rw [← e.target_eq],

feat(geometry/manifold/vector_bundle/basic): smooth vector bundles (#17611)

Definition of smooth vector bundle, and basic constructions (direct sum, pullback, core construction).

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

Diff

@@ -31,13 +31,13 @@ We provide the following operations on `trivialization`s.
 ## Implementation notes
 
 Previously, in mathlib, there was a structure `topological_vector_bundle.trivialization` which
-extended another structure `topological_fibre_bundle.trivialization` by a linearity hypothesis. As
+extended another structure `topological_fiber_bundle.trivialization` by a linearity hypothesis. As
 of PR #17359, we have changed this to a single structure `trivialization` (no namespace), together
 with a mixin class `trivialization.is_linear`.
 
-This permits all the *data* of a vector bundle to be held at the level of fibre bundles, so that the
+This permits all the *data* of a vector bundle to be held at the level of fiber bundles, so that the
 same trivializations can underlie an object's structure as (say) a vector bundle over `ℂ` and as a
-vector bundle over `ℝ`, as well as its structure simply as a fibre bundle.
+vector bundle over `ℝ`, as well as its structure simply as a fiber bundle.
 
 This might be a little surprising, given the general trend of the library to ever-increased
 bundling.  But in this case the typical motivation for more bundling does not apply: there is no

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -5,7 +5,7 @@ Authors: Sébastien Gouëzel
 -/
 import Data.Bundle
 import Topology.Algebra.Order.Field
-import Topology.LocalHomeomorph
+import Topology.PartialHomeomorph
 
 #align_import topology.fiber_bundle.trivialization from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -145,7 +145,7 @@ theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toPartialEquiv.symm x) = x.1 :=
   by
   have := (e.coe_fst (e.to_local_equiv.map_target hx)).symm
-  rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this 
+  rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this
 #align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_apply
 -/

bump to nightly-2023-12-14-06

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

a154f5e6

Diff

@@ -69,7 +69,7 @@ have a topology on both the fiber and the base space. Through the construction
 `topological_fiber_prebundle F proj` it will be possible to promote a
 `pretrivialization F proj` to a `trivialization F proj`. -/
 @[ext, nolint has_nonempty_instance]
-structure Pretrivialization (proj : Z → B) extends LocalEquiv Z (B × F) where
+structure Pretrivialization (proj : Z → B) extends PartialEquiv Z (B × F) where
   open_target : IsOpen target
   baseSet : Set B
   open_baseSet : IsOpen base_set
@@ -88,7 +88,7 @@ variable {F} (e : Pretrivialization F proj) {x : Z}
 
 #print Pretrivialization.coe_coe /-
 @[simp, mfld_simps]
-theorem coe_coe : ⇑e.toLocalEquiv = e :=
+theorem coe_coe : ⇑e.toPartialEquiv = e :=
   rfl
 #align pretrivialization.coe_coe Pretrivialization.coe_coe
 -/
@@ -131,7 +131,7 @@ theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
 #print Pretrivialization.setSymm /-
 /-- Composition of inverse and coercion from the subtype of the target. -/
 def setSymm : e.target → Z :=
-  e.target.restrict e.toLocalEquiv.symm
+  e.target.restrict e.toPartialEquiv.symm
 #align pretrivialization.set_symm Pretrivialization.setSymm
 -/
 
@@ -142,7 +142,7 @@ theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
 -/
 
 #print Pretrivialization.proj_symm_apply /-
-theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEquiv.symm x) = x.1 :=
+theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toPartialEquiv.symm x) = x.1 :=
   by
   have := (e.coe_fst (e.to_local_equiv.map_target hx)).symm
   rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this 
@@ -151,7 +151,7 @@ theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEqui
 
 #print Pretrivialization.proj_symm_apply' /-
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    proj (e.toLocalEquiv.symm (b, x)) = b :=
+    proj (e.toPartialEquiv.symm (b, x)) = b :=
   e.proj_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.proj_symm_apply' Pretrivialization.proj_symm_apply'
 -/
@@ -159,34 +159,34 @@ theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
 #print Pretrivialization.proj_surjOn_baseSet /-
 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet := fun b hb =>
   let ⟨y⟩ := ‹Nonempty F›
-  ⟨e.toLocalEquiv.symm (b, y), e.toLocalEquiv.map_target <| e.mem_target.2 hb,
+  ⟨e.toPartialEquiv.symm (b, y), e.toPartialEquiv.map_target <| e.mem_target.2 hb,
     e.proj_symm_apply' hb⟩
 #align pretrivialization.proj_surj_on_base_set Pretrivialization.proj_surjOn_baseSet
 -/
 
 #print Pretrivialization.apply_symm_apply /-
-theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalEquiv.symm x) = x :=
-  e.toLocalEquiv.right_inv hx
+theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toPartialEquiv.symm x) = x :=
+  e.toPartialEquiv.right_inv hx
 #align pretrivialization.apply_symm_apply Pretrivialization.apply_symm_apply
 -/
 
 #print Pretrivialization.apply_symm_apply' /-
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    e (e.toLocalEquiv.symm (b, x)) = (b, x) :=
+    e (e.toPartialEquiv.symm (b, x)) = (b, x) :=
   e.apply_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.apply_symm_apply' Pretrivialization.apply_symm_apply'
 -/
 
 #print Pretrivialization.symm_apply_apply /-
-theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toLocalEquiv.symm (e x) = x :=
-  e.toLocalEquiv.left_inv hx
+theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toPartialEquiv.symm (e x) = x :=
+  e.toPartialEquiv.left_inv hx
 #align pretrivialization.symm_apply_apply Pretrivialization.symm_apply_apply
 -/
 
 #print Pretrivialization.symm_apply_mk_proj /-
 @[simp, mfld_simps]
 theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
-    e.toLocalEquiv.symm (proj x, (e x).2) = x := by
+    e.toPartialEquiv.symm (proj x, (e x).2) = x := by
   rw [← e.coe_fst ex, Prod.mk.eta, ← e.coe_coe, e.to_local_equiv.left_inv ex]
 #align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_proj
 -/
@@ -194,10 +194,10 @@ theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
 #print Pretrivialization.preimage_symm_proj_baseSet /-
 @[simp, mfld_simps]
 theorem preimage_symm_proj_baseSet :
-    e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target :=
+    e.toPartialEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target :=
   by
   refine' inter_eq_right_iff_subset.mpr fun x hx => _
-  simp only [mem_preimage, LocalEquiv.invFun_as_coe, e.proj_symm_apply hx]
+  simp only [mem_preimage, PartialEquiv.invFun_as_coe, e.proj_symm_apply hx]
   exact e.mem_target.mp hx
 #align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSet
 -/
@@ -207,7 +207,7 @@ theorem preimage_symm_proj_baseSet :
 #print Pretrivialization.preimage_symm_proj_inter /-
 @[simp, mfld_simps]
 theorem preimage_symm_proj_inter (s : Set B) :
-    e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' s) ∩ e.baseSet ×ˢ univ = (s ∩ e.baseSet) ×ˢ univ :=
+    e.toPartialEquiv.symm ⁻¹' (proj ⁻¹' s) ∩ e.baseSet ×ˢ univ = (s ∩ e.baseSet) ×ˢ univ :=
   by
   ext ⟨x, y⟩
   suffices x ∈ e.base_set → (proj (e.to_local_equiv.symm (x, y)) ∈ s ↔ x ∈ s) by
@@ -220,7 +220,7 @@ theorem preimage_symm_proj_inter (s : Set B) :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Pretrivialization.target_inter_preimage_symm_source_eq /-
 theorem target_inter_preimage_symm_source_eq (e f : Pretrivialization F proj) :
-    f.target ∩ f.toLocalEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
+    f.target ∩ f.toPartialEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [inter_comm, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]
 #align pretrivialization.target_inter_preimage_symm_source_eq Pretrivialization.target_inter_preimage_symm_source_eq
 -/
@@ -228,23 +228,24 @@ theorem target_inter_preimage_symm_source_eq (e f : Pretrivialization F proj) :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Pretrivialization.trans_source /-
 theorem trans_source (e f : Pretrivialization F proj) :
-    (f.toLocalEquiv.symm.trans e.toLocalEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
-  rw [LocalEquiv.trans_source, LocalEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
+    (f.toPartialEquiv.symm.trans e.toPartialEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
+  rw [PartialEquiv.trans_source, PartialEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
 #align pretrivialization.trans_source Pretrivialization.trans_source
 -/
 
 #print Pretrivialization.symm_trans_symm /-
 theorem symm_trans_symm (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm = e'.toLocalEquiv.symm.trans e.toLocalEquiv :=
-  by rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).symm =
+      e'.toPartialEquiv.symm.trans e.toPartialEquiv :=
+  by rw [PartialEquiv.trans_symm_eq_symm_trans_symm, PartialEquiv.symm_symm]
 #align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symm
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Pretrivialization.symm_trans_source_eq /-
 theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
-  rw [LocalEquiv.trans_source, e'.source_eq, LocalEquiv.symm_source, e.target_eq, inter_comm,
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
+  rw [PartialEquiv.trans_source, e'.source_eq, PartialEquiv.symm_source, e.target_eq, inter_comm,
     e.preimage_symm_proj_inter, inter_comm]
 #align pretrivialization.symm_trans_source_eq Pretrivialization.symm_trans_source_eq
 -/
@@ -252,8 +253,8 @@ theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Pretrivialization.symm_trans_target_eq /-
 theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
-  rw [← LocalEquiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
+  rw [← PartialEquiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
 #align pretrivialization.symm_trans_target_eq Pretrivialization.symm_trans_target_eq
 -/
 
@@ -281,7 +282,7 @@ theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSe
 
 #print Pretrivialization.symm_coe_proj /-
 theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π F E)) (h : x ∈ e'.baseSet) :
-    (e'.toLocalEquiv.symm (x, y)).1 = x :=
+    (e'.toPartialEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
 #align pretrivialization.symm_coe_proj Pretrivialization.symm_coe_proj
 -/
@@ -295,14 +296,14 @@ variable [∀ x, Zero (E x)]
 `B × F → total_space F E` of `e` on `e.base_set`. It is defined to be `0` outside `e.base_set`. -/
 protected noncomputable def symm (e : Pretrivialization F (π F E)) (b : B) (y : F) : E b :=
   if hb : b ∈ e.baseSet then
-    cast (congr_arg E (e.proj_symm_apply' hb)) (e.toLocalEquiv.symm (b, y)).2
+    cast (congr_arg E (e.proj_symm_apply' hb)) (e.toPartialEquiv.symm (b, y)).2
   else 0
 #align pretrivialization.symm Pretrivialization.symm
 -/
 
 #print Pretrivialization.symm_apply /-
 theorem symm_apply (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
+    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toPartialEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
 -/
@@ -323,7 +324,7 @@ theorem coe_symm_of_not_mem (e : Pretrivialization F (π F E)) {b : B} (hb : b 
 
 #print Pretrivialization.mk_symm /-
 theorem mk_symm (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    TotalSpace.mk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
+    TotalSpace.mk b (e.symm b y) = e.toPartialEquiv.symm (b, y) := by
   rw [e.symm_apply hb, total_space.mk_cast, total_space.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
 -/
@@ -510,7 +511,7 @@ theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toPartialHomeomorph.symm (p
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Trivialization.symm_trans_source_eq /-
 theorem symm_trans_source_eq (e e' : Trivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_source_eq e.toPretrivialization e'
 #align trivialization.symm_trans_source_eq Trivialization.symm_trans_source_eq
 -/
@@ -518,7 +519,7 @@ theorem symm_trans_source_eq (e e' : Trivialization F proj) :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Trivialization.symm_trans_target_eq /-
 theorem symm_trans_target_eq (e e' : Trivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_target_eq e.toPretrivialization e'
 #align trivialization.symm_trans_target_eq Trivialization.symm_trans_target_eq
 -/
@@ -664,11 +665,11 @@ protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ
 trivialization of `Z` containing `z`. -/
 theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z → X} {z : Z}
     (e : Trivialization F proj) (he : proj z ∈ e.baseSet)
-    (hf : ContinuousAt (f ∘ e.toLocalEquiv.symm) (e z)) : ContinuousAt f z :=
+    (hf : ContinuousAt (f ∘ e.toPartialEquiv.symm) (e z)) : ContinuousAt f z :=
   by
   have hez : z ∈ e.to_local_equiv.symm.target :=
     by
-    rw [LocalEquiv.symm_target, e.mem_source]
+    rw [PartialEquiv.symm_target, e.mem_source]
     exact he
   rwa [e.to_local_homeomorph.symm.continuous_at_iff_continuous_at_comp_right hez,
     PartialHomeomorph.symm_symm]
@@ -725,7 +726,7 @@ theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
 #print Trivialization.symm_apply_apply /-
 theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
     e'.toPartialHomeomorph.symm (e' x) = x :=
-  e'.toLocalEquiv.left_inv hx
+  e'.toPartialEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 -/

bump to nightly-2023-12-13-12

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

19154cfe

Diff

@@ -361,7 +361,7 @@ variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 sets of the form `proj ⁻¹' base_set` and `base_set × F`, acting trivially on the first coordinate.
 -/
 @[ext, nolint has_nonempty_instance]
-structure Trivialization (proj : Z → B) extends LocalHomeomorph Z (B × F) where
+structure Trivialization (proj : Z → B) extends PartialHomeomorph Z (B × F) where
   baseSet : Set B
   open_baseSet : IsOpen base_set
   source_eq : source = proj ⁻¹' base_set
@@ -400,7 +400,7 @@ theorem toPretrivialization_injective :
 
 #print Trivialization.coe_coe /-
 @[simp, mfld_simps]
-theorem coe_coe : ⇑e.toLocalHomeomorph = e :=
+theorem coe_coe : ⇑e.toPartialHomeomorph = e :=
   rfl
 #align trivialization.coe_coe Trivialization.coe_coe
 -/
@@ -443,13 +443,13 @@ theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
 #print Trivialization.source_inter_preimage_target_inter /-
 theorem source_inter_preimage_target_inter (s : Set (B × F)) :
     e.source ∩ e ⁻¹' (e.target ∩ s) = e.source ∩ e ⁻¹' s :=
-  e.toLocalHomeomorph.source_inter_preimage_target_inter s
+  e.toPartialHomeomorph.source_inter_preimage_target_inter s
 #align trivialization.source_inter_preimage_target_inter Trivialization.source_inter_preimage_target_inter
 -/
 
 #print Trivialization.coe_mk /-
 @[simp, mfld_simps]
-theorem coe_mk (e : LocalHomeomorph Z (B × F)) (i j k l m) (x : Z) :
+theorem coe_mk (e : PartialHomeomorph Z (B × F)) (i j k l m) (x : Z) :
     (Trivialization.mk e i j k l m : Trivialization F proj) x = e x :=
   rfl
 #align trivialization.coe_mk Trivialization.coe_mk
@@ -462,20 +462,21 @@ theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet :=
 -/
 
 #print Trivialization.map_target /-
-theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toLocalHomeomorph.symm x ∈ e.source :=
-  e.toLocalHomeomorph.map_target hx
+theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toPartialHomeomorph.symm x ∈ e.source :=
+  e.toPartialHomeomorph.map_target hx
 #align trivialization.map_target Trivialization.map_target
 -/
 
 #print Trivialization.proj_symm_apply /-
-theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalHomeomorph.symm x) = x.1 :=
+theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) :
+    proj (e.toPartialHomeomorph.symm x) = x.1 :=
   e.toPretrivialization.proj_symm_apply hx
 #align trivialization.proj_symm_apply Trivialization.proj_symm_apply
 -/
 
 #print Trivialization.proj_symm_apply' /-
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    proj (e.toLocalHomeomorph.symm (b, x)) = b :=
+    proj (e.toPartialHomeomorph.symm (b, x)) = b :=
   e.toPretrivialization.proj_symm_apply' hx
 #align trivialization.proj_symm_apply' Trivialization.proj_symm_apply'
 -/
@@ -487,21 +488,21 @@ theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet :=
 -/
 
 #print Trivialization.apply_symm_apply /-
-theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalHomeomorph.symm x) = x :=
-  e.toLocalHomeomorph.right_inv hx
+theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toPartialHomeomorph.symm x) = x :=
+  e.toPartialHomeomorph.right_inv hx
 #align trivialization.apply_symm_apply Trivialization.apply_symm_apply
 -/
 
 #print Trivialization.apply_symm_apply' /-
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    e (e.toLocalHomeomorph.symm (b, x)) = (b, x) :=
+    e (e.toPartialHomeomorph.symm (b, x)) = (b, x) :=
   e.toPretrivialization.apply_symm_apply' hx
 #align trivialization.apply_symm_apply' Trivialization.apply_symm_apply'
 -/
 
 #print Trivialization.symm_apply_mk_proj /-
 @[simp, mfld_simps]
-theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toLocalHomeomorph.symm (proj x, (e x).2) = x :=
+theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toPartialHomeomorph.symm (proj x, (e x).2) = x :=
   e.toPretrivialization.symm_apply_mk_proj ex
 #align trivialization.symm_apply_mk_proj Trivialization.symm_apply_mk_proj
 -/
@@ -563,7 +564,7 @@ theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
 #print Trivialization.preimageHomeomorph /-
 /-- The preimage of a subset of the base set is homeomorphic to the product with the fiber. -/
 def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ s × F :=
-  (e.toLocalHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
+  (e.toPartialHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
         (e.image_preimage_eq_prod_univ hb)).trans
     ((Homeomorph.Set.prod s univ).trans ((Homeomorph.refl s).prodCongr (Homeomorph.Set.univ F)))
 #align trivialization.preimage_homeomorph Trivialization.preimageHomeomorph
@@ -647,7 +648,7 @@ theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
 protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
     Trivialization F (proj ∘ h)
     where
-  toLocalHomeomorph := h.toLocalHomeomorph.trans e.toLocalHomeomorph
+  toPartialHomeomorph := h.toPartialHomeomorph.trans e.toPartialHomeomorph
   baseSet := e.baseSet
   open_baseSet := e.open_baseSet
   source_eq := by simp [e.source_eq, preimage_preimage]
@@ -670,7 +671,7 @@ theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z →
     rw [LocalEquiv.symm_target, e.mem_source]
     exact he
   rwa [e.to_local_homeomorph.symm.continuous_at_iff_continuous_at_comp_right hez,
-    LocalHomeomorph.symm_symm]
+    PartialHomeomorph.symm_symm]
 #align trivialization.continuous_at_of_comp_right Trivialization.continuousAt_of_comp_right
 -/
 
@@ -723,7 +724,7 @@ theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
 
 #print Trivialization.symm_apply_apply /-
 theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
-    e'.toLocalHomeomorph.symm (e' x) = x :=
+    e'.toPartialHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 -/
@@ -731,7 +732,7 @@ theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
 #print Trivialization.symm_coe_proj /-
 @[simp, mfld_simps]
 theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π F E)) (h : x ∈ e.baseSet) :
-    (e.toLocalHomeomorph.symm (x, y)).1 = x :=
+    (e.toPartialHomeomorph.symm (x, y)).1 = x :=
   e.proj_symm_apply' h
 #align trivialization.symm_coe_proj Trivialization.symm_coe_proj
 -/
@@ -751,7 +752,7 @@ protected noncomputable def symm (e : Trivialization F (π F E)) (b : B) (y : F)
 
 #print Trivialization.symm_apply /-
 theorem symm_apply (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
+    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toPartialHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
 -/
@@ -765,7 +766,7 @@ theorem symm_apply_of_not_mem (e : Trivialization F (π F E)) {b : B} (hb : b 
 
 #print Trivialization.mk_symm /-
 theorem mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    TotalSpace.mk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
+    TotalSpace.mk b (e.symm b y) = e.toPartialHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
 -/
@@ -816,7 +817,7 @@ that sends `p : Z` to `((e p).1, h (e p).2)`. -/
 def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') : Trivialization F' proj
     where
-  toLocalHomeomorph := e.toLocalHomeomorph.transHomeomorph <| (Homeomorph.refl _).prodCongr h
+  toPartialHomeomorph := e.toPartialHomeomorph.transHomeomorph <| (Homeomorph.refl _).prodCongr h
   baseSet := e.baseSet
   open_baseSet := e.open_baseSet
   source_eq := e.source_eq
@@ -837,14 +838,14 @@ theorem transFiberHomeomorph_apply {F' : Type _} [TopologicalSpace F'] (e : Triv
 /-- Coordinate transformation in the fiber induced by a pair of bundle trivializations. See also
 `trivialization.coord_change_homeomorph` for a version bundled as `F ≃ₜ F`. -/
 def coordChange (e₁ e₂ : Trivialization F proj) (b : B) (x : F) : F :=
-  (e₂ <| e₁.toLocalHomeomorph.symm (b, x)).2
+  (e₂ <| e₁.toPartialHomeomorph.symm (b, x)).2
 #align trivialization.coord_change Trivialization.coordChange
 -/
 
 #print Trivialization.mk_coordChange /-
 theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
-    (b, e₁.coordChange e₂ b x) = e₂ (e₁.toLocalHomeomorph.symm (b, x)) :=
+    (b, e₁.coordChange e₂ b x) = e₂ (e₁.toPartialHomeomorph.symm (b, x)) :=
   by
   refine' Prod.ext _ rfl
   rw [e₂.coe_fst', ← e₁.coe_fst', e₁.apply_symm_apply' h₁]
@@ -927,7 +928,7 @@ variable {F} {B' : Type _} [TopologicalSpace B']
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Trivialization.isImage_preimage_prod /-
 theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
-    e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
+    e.toPartialHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
 #align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prod
 -/
 
@@ -936,7 +937,7 @@ theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
 protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s) :
     Trivialization F proj
     where
-  toLocalHomeomorph :=
+  toPartialHomeomorph :=
     ((e.isImage_preimage_prod s).symm.restr (IsOpen.inter e.open_target (hs.Prod isOpen_univ))).symm
   baseSet := e.baseSet ∩ s
   open_baseSet := IsOpen.inter e.open_baseSet hs
@@ -967,8 +968,8 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
     (Hs : e.baseSet ∩ frontier s = e'.baseSet ∩ frontier s)
     (Heq : EqOn e e' <| proj ⁻¹' (e.baseSet ∩ frontier s)) : Trivialization F proj
     where
-  toLocalHomeomorph :=
-    e.toLocalHomeomorph.piecewise e'.toLocalHomeomorph (proj ⁻¹' s) (s ×ˢ univ)
+  toPartialHomeomorph :=
+    e.toPartialHomeomorph.piecewise e'.toPartialHomeomorph (proj ⁻¹' s) (s ×ˢ univ)
       (e.isImage_preimage_prod s) (e'.isImage_preimage_prod s)
       (by rw [e.frontier_preimage, e'.frontier_preimage, Hs]) (by rwa [e.frontier_preimage])
   baseSet := s.ite e.baseSet e'.baseSet
@@ -1021,8 +1022,8 @@ base sets. -/
 noncomputable def disjointUnion (e e' : Trivialization F proj) (H : Disjoint e.baseSet e'.baseSet) :
     Trivialization F proj
     where
-  toLocalHomeomorph :=
-    e.toLocalHomeomorph.disjointUnion e'.toLocalHomeomorph
+  toPartialHomeomorph :=
+    e.toPartialHomeomorph.disjointUnion e'.toPartialHomeomorph
       (by rw [e.source_eq, e'.source_eq]; exact H.preimage _)
       (by
         rw [e.target_eq, e'.target_eq, disjoint_iff_inf_le]

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Data.Bundle
-import Mathbin.Topology.Algebra.Order.Field
-import Mathbin.Topology.LocalHomeomorph
+import Data.Bundle
+import Topology.Algebra.Order.Field
+import Topology.LocalHomeomorph
 
 #align_import topology.fiber_bundle.trivialization from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! 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.Data.Bundle
 import Mathbin.Topology.Algebra.Order.Field
 import Mathbin.Topology.LocalHomeomorph
 
+#align_import topology.fiber_bundle.trivialization from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-!
 # Trivializations

bump to nightly-2023-07-04-01

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

05318d71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -260,9 +260,10 @@ theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
 #align pretrivialization.symm_trans_target_eq Pretrivialization.symm_trans_target_eq
 -/
 
-variable {B F} (e' : Pretrivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
+variable {B F} (e' : Pretrivialization F (π F E)) {x' : TotalSpace F E} {b : B} {y : E b}
 
 #print Pretrivialization.coe_mem_source /-
+@[simp]
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align pretrivialization.coe_mem_source Pretrivialization.coe_mem_source
@@ -282,7 +283,7 @@ theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSe
 -/
 
 #print Pretrivialization.symm_coe_proj /-
-theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π E)) (h : x ∈ e'.baseSet) :
+theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π F E)) (h : x ∈ e'.baseSet) :
     (e'.toLocalEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
 #align pretrivialization.symm_coe_proj Pretrivialization.symm_coe_proj
@@ -294,8 +295,8 @@ variable [∀ x, Zero (E x)]
 
 #print Pretrivialization.symm /-
 /-- A fiberwise inverse to `e`. This is the function `F → E b` that induces a local inverse
-`B × F → total_space E` of `e` on `e.base_set`. It is defined to be `0` outside `e.base_set`. -/
-protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F) : E b :=
+`B × F → total_space F E` of `e` on `e.base_set`. It is defined to be `0` outside `e.base_set`. -/
+protected noncomputable def symm (e : Pretrivialization F (π F E)) (b : B) (y : F) : E b :=
   if hb : b ∈ e.baseSet then
     cast (congr_arg E (e.proj_symm_apply' hb)) (e.toLocalEquiv.symm (b, y)).2
   else 0
@@ -303,51 +304,50 @@ protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F
 -/
 
 #print Pretrivialization.symm_apply /-
-theorem symm_apply (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+theorem symm_apply (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
 -/
 
 #print Pretrivialization.symm_apply_of_not_mem /-
-theorem symm_apply_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
-    e.symm b y = 0 :=
+theorem symm_apply_of_not_mem (e : Pretrivialization F (π F E)) {b : B} (hb : b ∉ e.baseSet)
+    (y : F) : e.symm b y = 0 :=
   dif_neg hb
 #align pretrivialization.symm_apply_of_not_mem Pretrivialization.symm_apply_of_not_mem
 -/
 
 #print Pretrivialization.coe_symm_of_not_mem /-
-theorem coe_symm_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) :
+theorem coe_symm_of_not_mem (e : Pretrivialization F (π F E)) {b : B} (hb : b ∉ e.baseSet) :
     (e.symm b : F → E b) = 0 :=
   funext fun y => dif_neg hb
 #align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_mem
 -/
 
 #print Pretrivialization.mk_symm /-
-theorem mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    totalSpaceMk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
+theorem mk_symm (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    TotalSpace.mk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
   rw [e.symm_apply hb, total_space.mk_cast, total_space.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
 -/
 
 #print Pretrivialization.symm_proj_apply /-
-theorem symm_proj_apply (e : Pretrivialization F (π E)) (z : TotalSpace E)
+theorem symm_proj_apply (e : Pretrivialization F (π F E)) (z : TotalSpace F E)
     (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 := by
   rw [e.symm_apply hz, cast_eq_iff_heq, e.mk_proj_snd' hz, e.symm_apply_apply (e.mem_source.mpr hz)]
 #align pretrivialization.symm_proj_apply Pretrivialization.symm_proj_apply
 -/
 
 #print Pretrivialization.symm_apply_apply_mk /-
-theorem symm_apply_apply_mk (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
-    e.symm b (e (totalSpaceMk b y)).2 = y :=
-  e.symm_proj_apply (totalSpaceMk b y) hb
+theorem symm_apply_apply_mk (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet)
+    (y : E b) : e.symm b (e ⟨b, y⟩).2 = y :=
+  e.symm_proj_apply ⟨b, y⟩ hb
 #align pretrivialization.symm_apply_apply_mk Pretrivialization.symm_apply_apply_mk
 -/
 
 #print Pretrivialization.apply_mk_symm /-
-theorem apply_mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e (totalSpaceMk b (e.symm b y)) = (b, y) := by
-  rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
+theorem apply_mk_symm (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    e ⟨b, e.symm b y⟩ = (b, y) := by rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
 #align pretrivialization.apply_mk_symm Pretrivialization.apply_mk_symm
 -/
 
@@ -355,7 +355,7 @@ end Zero
 
 end Pretrivialization
 
-variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace E)]
+variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 
 #print Trivialization /-
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -691,7 +691,7 @@ theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z
 #align trivialization.continuous_at_of_comp_left Trivialization.continuousAt_of_comp_left
 -/
 
-variable {E} (e' : Trivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
+variable {E} (e' : Trivialization F (π F E)) {x' : TotalSpace F E} {b : B} {y : E b}
 
 #print Trivialization.continuousOn /-
 protected theorem continuousOn : ContinuousOn e' e'.source :=
@@ -725,7 +725,7 @@ theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
 -/
 
 #print Trivialization.symm_apply_apply /-
-theorem symm_apply_apply {x : TotalSpace E} (hx : x ∈ e'.source) :
+theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
     e'.toLocalHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
@@ -733,7 +733,7 @@ theorem symm_apply_apply {x : TotalSpace E} (hx : x ∈ e'.source) :
 
 #print Trivialization.symm_coe_proj /-
 @[simp, mfld_simps]
-theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π E)) (h : x ∈ e.baseSet) :
+theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π F E)) (h : x ∈ e.baseSet) :
     (e.toLocalHomeomorph.symm (x, y)).1 = x :=
   e.proj_symm_apply' h
 #align trivialization.symm_coe_proj Trivialization.symm_coe_proj
@@ -745,50 +745,51 @@ variable [∀ x, Zero (E x)]
 
 #print Trivialization.symm /-
 /-- A fiberwise inverse to `e'`. The function `F → E x` that induces a local inverse
-`B × F → total_space E` of `e'` on `e'.base_set`. It is defined to be `0` outside `e'.base_set`. -/
-protected noncomputable def symm (e : Trivialization F (π E)) (b : B) (y : F) : E b :=
+`B × F → total_space F E` of `e'` on `e'.base_set`. It is defined to be `0` outside
+`e'.base_set`. -/
+protected noncomputable def symm (e : Trivialization F (π F E)) (b : B) (y : F) : E b :=
   e.toPretrivialization.symm b y
 #align trivialization.symm Trivialization.symm
 -/
 
 #print Trivialization.symm_apply /-
-theorem symm_apply (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+theorem symm_apply (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
 -/
 
 #print Trivialization.symm_apply_of_not_mem /-
-theorem symm_apply_of_not_mem (e : Trivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
+theorem symm_apply_of_not_mem (e : Trivialization F (π F E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_mem
 -/
 
 #print Trivialization.mk_symm /-
-theorem mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    totalSpaceMk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
+theorem mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    TotalSpace.mk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
 -/
 
 #print Trivialization.symm_proj_apply /-
-theorem symm_proj_apply (e : Trivialization F (π E)) (z : TotalSpace E) (hz : z.proj ∈ e.baseSet) :
-    e.symm z.proj (e z).2 = z.2 :=
+theorem symm_proj_apply (e : Trivialization F (π F E)) (z : TotalSpace F E)
+    (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 :=
   e.toPretrivialization.symm_proj_apply z hz
 #align trivialization.symm_proj_apply Trivialization.symm_proj_apply
 -/
 
 #print Trivialization.symm_apply_apply_mk /-
-theorem symm_apply_apply_mk (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
-    e.symm b (e (totalSpaceMk b y)).2 = y :=
-  e.symm_proj_apply (totalSpaceMk b y) hb
+theorem symm_apply_apply_mk (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
+    e.symm b (e ⟨b, y⟩).2 = y :=
+  e.symm_proj_apply ⟨b, y⟩ hb
 #align trivialization.symm_apply_apply_mk Trivialization.symm_apply_apply_mk
 -/
 
 #print Trivialization.apply_mk_symm /-
-theorem apply_mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e (totalSpaceMk b (e.symm b y)) = (b, y) :=
+theorem apply_mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    e ⟨b, e.symm b y⟩ = (b, y) :=
   e.toPretrivialization.apply_mk_symm hb y
 #align trivialization.apply_mk_symm Trivialization.apply_mk_symm
 -/
@@ -796,12 +797,12 @@ theorem apply_mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSe
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Trivialization.continuousOn_symm /-
-theorem continuousOn_symm (e : Trivialization F (π E)) :
-    ContinuousOn (fun z : B × F => totalSpaceMk z.1 (e.symm z.1 z.2)) (e.baseSet ×ˢ univ) :=
+theorem continuousOn_symm (e : Trivialization F (π F E)) :
+    ContinuousOn (fun z : B × F => (total_space.mk' F) z.1 (e.symm z.1 z.2)) (e.baseSet ×ˢ univ) :=
   by
   have :
     ∀ (z : B × F) (hz : z ∈ e.base_set ×ˢ (univ : Set F)),
-      total_space_mk z.1 (e.symm z.1 z.2) = e.to_local_homeomorph.symm z :=
+      total_space.mk z.1 (e.symm z.1 z.2) = e.to_local_homeomorph.symm z :=
     by rintro x ⟨hx : x.1 ∈ e.base_set, _⟩; simp_rw [e.mk_symm hx, Prod.mk.eta]
   refine' ContinuousOn.congr _ this
   rw [← e.target_eq]

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -89,33 +89,47 @@ instance : CoeFun (Pretrivialization F proj) fun _ => Z → B × F :=
 
 variable {F} (e : Pretrivialization F proj) {x : Z}
 
+#print Pretrivialization.coe_coe /-
 @[simp, mfld_simps]
 theorem coe_coe : ⇑e.toLocalEquiv = e :=
   rfl
 #align pretrivialization.coe_coe Pretrivialization.coe_coe
+-/
 
+#print Pretrivialization.coe_fst /-
 @[simp, mfld_simps]
 theorem coe_fst (ex : x ∈ e.source) : (e x).1 = proj x :=
   e.proj_toFun x ex
 #align pretrivialization.coe_fst Pretrivialization.coe_fst
+-/
 
+#print Pretrivialization.mem_source /-
 theorem mem_source : x ∈ e.source ↔ proj x ∈ e.baseSet := by rw [e.source_eq, mem_preimage]
 #align pretrivialization.mem_source Pretrivialization.mem_source
+-/
 
+#print Pretrivialization.coe_fst' /-
 theorem coe_fst' (ex : proj x ∈ e.baseSet) : (e x).1 = proj x :=
   e.coe_fst (e.mem_source.2 ex)
 #align pretrivialization.coe_fst' Pretrivialization.coe_fst'
+-/
 
+#print Pretrivialization.eqOn /-
 protected theorem eqOn : EqOn (Prod.fst ∘ e) proj e.source := fun x hx => e.coe_fst hx
 #align pretrivialization.eq_on Pretrivialization.eqOn
+-/
 
+#print Pretrivialization.mk_proj_snd /-
 theorem mk_proj_snd (ex : x ∈ e.source) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst ex).symm rfl
 #align pretrivialization.mk_proj_snd Pretrivialization.mk_proj_snd
+-/
 
+#print Pretrivialization.mk_proj_snd' /-
 theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst' ex).symm rfl
 #align pretrivialization.mk_proj_snd' Pretrivialization.mk_proj_snd'
+-/
 
 #print Pretrivialization.setSymm /-
 /-- Composition of inverse and coercion from the subtype of the target. -/
@@ -124,46 +138,63 @@ def setSymm : e.target → Z :=
 #align pretrivialization.set_symm Pretrivialization.setSymm
 -/
 
+#print Pretrivialization.mem_target /-
 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
   rw [e.target_eq, prod_univ, mem_preimage]
 #align pretrivialization.mem_target Pretrivialization.mem_target
+-/
 
+#print Pretrivialization.proj_symm_apply /-
 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEquiv.symm x) = x.1 :=
   by
   have := (e.coe_fst (e.to_local_equiv.map_target hx)).symm
   rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this 
 #align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_apply
+-/
 
+#print Pretrivialization.proj_symm_apply' /-
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     proj (e.toLocalEquiv.symm (b, x)) = b :=
   e.proj_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.proj_symm_apply' Pretrivialization.proj_symm_apply'
+-/
 
+#print Pretrivialization.proj_surjOn_baseSet /-
 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet := fun b hb =>
   let ⟨y⟩ := ‹Nonempty F›
   ⟨e.toLocalEquiv.symm (b, y), e.toLocalEquiv.map_target <| e.mem_target.2 hb,
     e.proj_symm_apply' hb⟩
 #align pretrivialization.proj_surj_on_base_set Pretrivialization.proj_surjOn_baseSet
+-/
 
+#print Pretrivialization.apply_symm_apply /-
 theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalEquiv.symm x) = x :=
   e.toLocalEquiv.right_inv hx
 #align pretrivialization.apply_symm_apply Pretrivialization.apply_symm_apply
+-/
 
+#print Pretrivialization.apply_symm_apply' /-
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     e (e.toLocalEquiv.symm (b, x)) = (b, x) :=
   e.apply_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.apply_symm_apply' Pretrivialization.apply_symm_apply'
+-/
 
+#print Pretrivialization.symm_apply_apply /-
 theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toLocalEquiv.symm (e x) = x :=
   e.toLocalEquiv.left_inv hx
 #align pretrivialization.symm_apply_apply Pretrivialization.symm_apply_apply
+-/
 
+#print Pretrivialization.symm_apply_mk_proj /-
 @[simp, mfld_simps]
 theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
     e.toLocalEquiv.symm (proj x, (e x).2) = x := by
   rw [← e.coe_fst ex, Prod.mk.eta, ← e.coe_coe, e.to_local_equiv.left_inv ex]
 #align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_proj
+-/
 
+#print Pretrivialization.preimage_symm_proj_baseSet /-
 @[simp, mfld_simps]
 theorem preimage_symm_proj_baseSet :
     e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target :=
@@ -172,9 +203,11 @@ theorem preimage_symm_proj_baseSet :
   simp only [mem_preimage, LocalEquiv.invFun_as_coe, e.proj_symm_apply hx]
   exact e.mem_target.mp hx
 #align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSet
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Pretrivialization.preimage_symm_proj_inter /-
 @[simp, mfld_simps]
 theorem preimage_symm_proj_inter (s : Set B) :
     e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' s) ∩ e.baseSet ×ˢ univ = (s ∩ e.baseSet) ×ˢ univ :=
@@ -185,56 +218,75 @@ theorem preimage_symm_proj_inter (s : Set B) :
   intro h
   rw [e.proj_symm_apply' h]
 #align pretrivialization.preimage_symm_proj_inter Pretrivialization.preimage_symm_proj_inter
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Pretrivialization.target_inter_preimage_symm_source_eq /-
 theorem target_inter_preimage_symm_source_eq (e f : Pretrivialization F proj) :
     f.target ∩ f.toLocalEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [inter_comm, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]
 #align pretrivialization.target_inter_preimage_symm_source_eq Pretrivialization.target_inter_preimage_symm_source_eq
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Pretrivialization.trans_source /-
 theorem trans_source (e f : Pretrivialization F proj) :
     (f.toLocalEquiv.symm.trans e.toLocalEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [LocalEquiv.trans_source, LocalEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
 #align pretrivialization.trans_source Pretrivialization.trans_source
+-/
 
+#print Pretrivialization.symm_trans_symm /-
 theorem symm_trans_symm (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm = e'.toLocalEquiv.symm.trans e.toLocalEquiv :=
   by rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
 #align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symm
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Pretrivialization.symm_trans_source_eq /-
 theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
   rw [LocalEquiv.trans_source, e'.source_eq, LocalEquiv.symm_source, e.target_eq, inter_comm,
     e.preimage_symm_proj_inter, inter_comm]
 #align pretrivialization.symm_trans_source_eq Pretrivialization.symm_trans_source_eq
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Pretrivialization.symm_trans_target_eq /-
 theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
   rw [← LocalEquiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
 #align pretrivialization.symm_trans_target_eq Pretrivialization.symm_trans_target_eq
+-/
 
 variable {B F} (e' : Pretrivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
 
+#print Pretrivialization.coe_mem_source /-
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align pretrivialization.coe_mem_source Pretrivialization.coe_mem_source
+-/
 
+#print Pretrivialization.coe_coe_fst /-
 @[simp, mfld_simps]
 theorem coe_coe_fst (hb : b ∈ e'.baseSet) : (e' y).1 = b :=
   e'.coe_fst (e'.mem_source.2 hb)
 #align pretrivialization.coe_coe_fst Pretrivialization.coe_coe_fst
+-/
 
+#print Pretrivialization.mk_mem_target /-
 theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSet :=
   e'.mem_target
 #align pretrivialization.mk_mem_target Pretrivialization.mk_mem_target
+-/
 
+#print Pretrivialization.symm_coe_proj /-
 theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π E)) (h : x ∈ e'.baseSet) :
     (e'.toLocalEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
 #align pretrivialization.symm_coe_proj Pretrivialization.symm_coe_proj
+-/
 
 section Zero
 
@@ -250,40 +302,54 @@ protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F
 #align pretrivialization.symm Pretrivialization.symm
 -/
 
+#print Pretrivialization.symm_apply /-
 theorem symm_apply (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
+-/
 
+#print Pretrivialization.symm_apply_of_not_mem /-
 theorem symm_apply_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align pretrivialization.symm_apply_of_not_mem Pretrivialization.symm_apply_of_not_mem
+-/
 
+#print Pretrivialization.coe_symm_of_not_mem /-
 theorem coe_symm_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) :
     (e.symm b : F → E b) = 0 :=
   funext fun y => dif_neg hb
 #align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_mem
+-/
 
+#print Pretrivialization.mk_symm /-
 theorem mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     totalSpaceMk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
   rw [e.symm_apply hb, total_space.mk_cast, total_space.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
+-/
 
+#print Pretrivialization.symm_proj_apply /-
 theorem symm_proj_apply (e : Pretrivialization F (π E)) (z : TotalSpace E)
     (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 := by
   rw [e.symm_apply hz, cast_eq_iff_heq, e.mk_proj_snd' hz, e.symm_apply_apply (e.mem_source.mpr hz)]
 #align pretrivialization.symm_proj_apply Pretrivialization.symm_proj_apply
+-/
 
+#print Pretrivialization.symm_apply_apply_mk /-
 theorem symm_apply_apply_mk (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
     e.symm b (e (totalSpaceMk b y)).2 = y :=
   e.symm_proj_apply (totalSpaceMk b y) hb
 #align pretrivialization.symm_apply_apply_mk Pretrivialization.symm_apply_apply_mk
+-/
 
+#print Pretrivialization.apply_mk_symm /-
 theorem apply_mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e (totalSpaceMk b (e.symm b y)) = (b, y) := by
   rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
 #align pretrivialization.apply_mk_symm Pretrivialization.apply_mk_symm
+-/
 
 end Zero
 
@@ -324,6 +390,7 @@ instance : CoeFun (Trivialization F proj) fun _ => Z → B × F :=
 instance : Coe (Trivialization F proj) (Pretrivialization F proj) :=
   ⟨toPretrivialization⟩
 
+#print Trivialization.toPretrivialization_injective /-
 theorem toPretrivialization_injective :
     Function.Injective fun e : Trivialization F proj => e.toPretrivialization :=
   by
@@ -332,111 +399,159 @@ theorem toPretrivialization_injective :
     local_homeomorph.to_local_equiv_injective.eq_iff]
   exact id
 #align trivialization.to_pretrivialization_injective Trivialization.toPretrivialization_injective
+-/
 
+#print Trivialization.coe_coe /-
 @[simp, mfld_simps]
 theorem coe_coe : ⇑e.toLocalHomeomorph = e :=
   rfl
 #align trivialization.coe_coe Trivialization.coe_coe
+-/
 
+#print Trivialization.coe_fst /-
 @[simp, mfld_simps]
 theorem coe_fst (ex : x ∈ e.source) : (e x).1 = proj x :=
   e.proj_toFun x ex
 #align trivialization.coe_fst Trivialization.coe_fst
+-/
 
+#print Trivialization.eqOn /-
 protected theorem eqOn : EqOn (Prod.fst ∘ e) proj e.source := fun x hx => e.coe_fst hx
 #align trivialization.eq_on Trivialization.eqOn
+-/
 
+#print Trivialization.mem_source /-
 theorem mem_source : x ∈ e.source ↔ proj x ∈ e.baseSet := by rw [e.source_eq, mem_preimage]
 #align trivialization.mem_source Trivialization.mem_source
+-/
 
+#print Trivialization.coe_fst' /-
 theorem coe_fst' (ex : proj x ∈ e.baseSet) : (e x).1 = proj x :=
   e.coe_fst (e.mem_source.2 ex)
 #align trivialization.coe_fst' Trivialization.coe_fst'
+-/
 
+#print Trivialization.mk_proj_snd /-
 theorem mk_proj_snd (ex : x ∈ e.source) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst ex).symm rfl
 #align trivialization.mk_proj_snd Trivialization.mk_proj_snd
+-/
 
+#print Trivialization.mk_proj_snd' /-
 theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst' ex).symm rfl
 #align trivialization.mk_proj_snd' Trivialization.mk_proj_snd'
+-/
 
+#print Trivialization.source_inter_preimage_target_inter /-
 theorem source_inter_preimage_target_inter (s : Set (B × F)) :
     e.source ∩ e ⁻¹' (e.target ∩ s) = e.source ∩ e ⁻¹' s :=
   e.toLocalHomeomorph.source_inter_preimage_target_inter s
 #align trivialization.source_inter_preimage_target_inter Trivialization.source_inter_preimage_target_inter
+-/
 
+#print Trivialization.coe_mk /-
 @[simp, mfld_simps]
 theorem coe_mk (e : LocalHomeomorph Z (B × F)) (i j k l m) (x : Z) :
     (Trivialization.mk e i j k l m : Trivialization F proj) x = e x :=
   rfl
 #align trivialization.coe_mk Trivialization.coe_mk
+-/
 
+#print Trivialization.mem_target /-
 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet :=
   e.toPretrivialization.mem_target
 #align trivialization.mem_target Trivialization.mem_target
+-/
 
+#print Trivialization.map_target /-
 theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toLocalHomeomorph.symm x ∈ e.source :=
   e.toLocalHomeomorph.map_target hx
 #align trivialization.map_target Trivialization.map_target
+-/
 
+#print Trivialization.proj_symm_apply /-
 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalHomeomorph.symm x) = x.1 :=
   e.toPretrivialization.proj_symm_apply hx
 #align trivialization.proj_symm_apply Trivialization.proj_symm_apply
+-/
 
+#print Trivialization.proj_symm_apply' /-
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     proj (e.toLocalHomeomorph.symm (b, x)) = b :=
   e.toPretrivialization.proj_symm_apply' hx
 #align trivialization.proj_symm_apply' Trivialization.proj_symm_apply'
+-/
 
+#print Trivialization.proj_surjOn_baseSet /-
 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet :=
   e.toPretrivialization.proj_surjOn_baseSet
 #align trivialization.proj_surj_on_base_set Trivialization.proj_surjOn_baseSet
+-/
 
+#print Trivialization.apply_symm_apply /-
 theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalHomeomorph.symm x) = x :=
   e.toLocalHomeomorph.right_inv hx
 #align trivialization.apply_symm_apply Trivialization.apply_symm_apply
+-/
 
+#print Trivialization.apply_symm_apply' /-
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     e (e.toLocalHomeomorph.symm (b, x)) = (b, x) :=
   e.toPretrivialization.apply_symm_apply' hx
 #align trivialization.apply_symm_apply' Trivialization.apply_symm_apply'
+-/
 
+#print Trivialization.symm_apply_mk_proj /-
 @[simp, mfld_simps]
 theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toLocalHomeomorph.symm (proj x, (e x).2) = x :=
   e.toPretrivialization.symm_apply_mk_proj ex
 #align trivialization.symm_apply_mk_proj Trivialization.symm_apply_mk_proj
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Trivialization.symm_trans_source_eq /-
 theorem symm_trans_source_eq (e e' : Trivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_source_eq e.toPretrivialization e'
 #align trivialization.symm_trans_source_eq Trivialization.symm_trans_source_eq
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Trivialization.symm_trans_target_eq /-
 theorem symm_trans_target_eq (e e' : Trivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_target_eq e.toPretrivialization e'
 #align trivialization.symm_trans_target_eq Trivialization.symm_trans_target_eq
+-/
 
+#print Trivialization.coe_fst_eventuallyEq_proj /-
 theorem coe_fst_eventuallyEq_proj (ex : x ∈ e.source) : Prod.fst ∘ e =ᶠ[𝓝 x] proj :=
   mem_nhds_iff.2 ⟨e.source, fun y hy => e.coe_fst hy, e.open_source, ex⟩
 #align trivialization.coe_fst_eventually_eq_proj Trivialization.coe_fst_eventuallyEq_proj
+-/
 
+#print Trivialization.coe_fst_eventuallyEq_proj' /-
 theorem coe_fst_eventuallyEq_proj' (ex : proj x ∈ e.baseSet) : Prod.fst ∘ e =ᶠ[𝓝 x] proj :=
   e.coe_fst_eventuallyEq_proj (e.mem_source.2 ex)
 #align trivialization.coe_fst_eventually_eq_proj' Trivialization.coe_fst_eventuallyEq_proj'
+-/
 
+#print Trivialization.map_proj_nhds /-
 theorem map_proj_nhds (ex : x ∈ e.source) : map proj (𝓝 x) = 𝓝 (proj x) := by
   rw [← e.coe_fst ex, ← map_congr (e.coe_fst_eventually_eq_proj ex), ← map_map, ← e.coe_coe,
     e.to_local_homeomorph.map_nhds_eq ex, map_fst_nhds]
 #align trivialization.map_proj_nhds Trivialization.map_proj_nhds
+-/
 
+#print Trivialization.preimage_subset_source /-
 theorem preimage_subset_source {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ⊆ e.source :=
   fun p hp => e.mem_source.mpr (hb hp)
 #align trivialization.preimage_subset_source Trivialization.preimage_subset_source
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Trivialization.image_preimage_eq_prod_univ /-
 theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     e '' (proj ⁻¹' s) = s ×ˢ univ :=
   Subset.antisymm
@@ -446,69 +561,91 @@ theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     let hp' : p ∈ e.target := e.mem_target.mpr (hb hp.1)
     ⟨e.invFun p, mem_preimage.mpr ((e.proj_symm_apply hp').symm ▸ hp.1), e.apply_symm_apply hp'⟩
 #align trivialization.image_preimage_eq_prod_univ Trivialization.image_preimage_eq_prod_univ
+-/
 
+#print Trivialization.preimageHomeomorph /-
 /-- The preimage of a subset of the base set is homeomorphic to the product with the fiber. -/
 def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ s × F :=
   (e.toLocalHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
         (e.image_preimage_eq_prod_univ hb)).trans
     ((Homeomorph.Set.prod s univ).trans ((Homeomorph.refl s).prodCongr (Homeomorph.Set.univ F)))
 #align trivialization.preimage_homeomorph Trivialization.preimageHomeomorph
+-/
 
+#print Trivialization.preimageHomeomorph_apply /-
 @[simp]
 theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj ⁻¹' s) :
     e.preimageHomeomorph hb p = (⟨proj p, p.2⟩, (e p).2) :=
   Prod.ext (Subtype.ext (e.proj_toFun p (e.mem_source.mpr (hb p.2)))) rfl
 #align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_apply
+-/
 
+#print Trivialization.preimageHomeomorph_symm_apply /-
 @[simp]
 theorem preimageHomeomorph_symm_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : s × F) :
     (e.preimageHomeomorph hb).symm p = ⟨e.symm (p.1, p.2), ((e.preimageHomeomorph hb).symm p).2⟩ :=
   rfl
 #align trivialization.preimage_homeomorph_symm_apply Trivialization.preimageHomeomorph_symm_apply
+-/
 
+#print Trivialization.sourceHomeomorphBaseSetProd /-
 /-- The source is homeomorphic to the product of the base set with the fiber. -/
 def sourceHomeomorphBaseSetProd : e.source ≃ₜ e.baseSet × F :=
   (Homeomorph.setCongr e.source_eq).trans (e.preimageHomeomorph subset_rfl)
 #align trivialization.source_homeomorph_base_set_prod Trivialization.sourceHomeomorphBaseSetProd
+-/
 
+#print Trivialization.sourceHomeomorphBaseSetProd_apply /-
 @[simp]
 theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
     e.sourceHomeomorphBaseSetProd p = (⟨proj p, e.mem_source.mp p.2⟩, (e p).2) :=
   e.preimageHomeomorph_apply subset_rfl ⟨p, e.mem_source.mp p.2⟩
 #align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_apply
+-/
 
+#print Trivialization.sourceHomeomorphBaseSetProd_symm_apply /-
 @[simp]
 theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
     e.sourceHomeomorphBaseSetProd.symm p =
       ⟨e.symm (p.1, p.2), (e.sourceHomeomorphBaseSetProd.symm p).2⟩ :=
   rfl
 #align trivialization.source_homeomorph_base_set_prod_symm_apply Trivialization.sourceHomeomorphBaseSetProd_symm_apply
+-/
 
+#print Trivialization.preimageSingletonHomeomorph /-
 /-- Each fiber of a trivialization is homeomorphic to the specified fiber. -/
 def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b} ≃ₜ F :=
   (e.preimageHomeomorph (Set.singleton_subset_iff.mpr hb)).trans
     (((Homeomorph.homeomorphOfUnique ({b} : Set B) PUnit).prodCongr (Homeomorph.refl F)).trans
       (Homeomorph.punitProd F))
 #align trivialization.preimage_singleton_homeomorph Trivialization.preimageSingletonHomeomorph
+-/
 
+#print Trivialization.preimageSingletonHomeomorph_apply /-
 @[simp]
 theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : proj ⁻¹' {b}) :
     e.preimageSingletonHomeomorph hb p = (e p).2 :=
   rfl
 #align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_apply
+-/
 
+#print Trivialization.preimageSingletonHomeomorph_symm_apply /-
 @[simp]
 theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p : F) :
     (e.preimageSingletonHomeomorph hb).symm p =
       ⟨e.symm (b, p), by rw [mem_preimage, e.proj_symm_apply' hb, mem_singleton_iff]⟩ :=
   rfl
 #align trivialization.preimage_singleton_homeomorph_symm_apply Trivialization.preimageSingletonHomeomorph_symm_apply
+-/
 
+#print Trivialization.continuousAt_proj /-
 /-- In the domain of a bundle trivialization, the projection is continuous-/
 theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
   (e.map_proj_nhds ex).le
 #align trivialization.continuous_at_proj Trivialization.continuousAt_proj
+-/
 
+#print Trivialization.compHomeomorph /-
 /-- Composition of a `trivialization` and a `homeomorph`. -/
 protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
     Trivialization F (proj ∘ h)
@@ -522,7 +659,9 @@ protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ
     have hp : h p ∈ e.source := by simpa using hp
     simp [hp]
 #align trivialization.comp_homeomorph Trivialization.compHomeomorph
+-/
 
+#print Trivialization.continuousAt_of_comp_right /-
 /-- Read off the continuity of a function `f : Z → X` at `z : Z` by transferring via a
 trivialization of `Z` containing `z`. -/
 theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z → X} {z : Z}
@@ -536,7 +675,9 @@ theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z →
   rwa [e.to_local_homeomorph.symm.continuous_at_iff_continuous_at_comp_right hez,
     LocalHomeomorph.symm_symm]
 #align trivialization.continuous_at_of_comp_right Trivialization.continuousAt_of_comp_right
+-/
 
+#print Trivialization.continuousAt_of_comp_left /-
 /-- Read off the continuity of a function `f : X → Z` at `x : X` by transferring via a
 trivialization of `Z` containing `f x`. -/
 theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z} {x : X}
@@ -548,40 +689,55 @@ theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z
   rw [e.source_eq, ← preimage_comp]
   exact hf_proj.preimage_mem_nhds (e.open_base_set.mem_nhds he)
 #align trivialization.continuous_at_of_comp_left Trivialization.continuousAt_of_comp_left
+-/
 
 variable {E} (e' : Trivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
 
+#print Trivialization.continuousOn /-
 protected theorem continuousOn : ContinuousOn e' e'.source :=
   e'.continuous_toFun
 #align trivialization.continuous_on Trivialization.continuousOn
+-/
 
+#print Trivialization.coe_mem_source /-
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align trivialization.coe_mem_source Trivialization.coe_mem_source
+-/
 
+#print Trivialization.open_target' /-
 theorem open_target' : IsOpen e'.target := by rw [e'.target_eq];
   exact e'.open_base_set.prod isOpen_univ
 #align trivialization.open_target Trivialization.open_target'
+-/
 
+#print Trivialization.coe_coe_fst /-
 @[simp, mfld_simps]
 theorem coe_coe_fst (hb : b ∈ e'.baseSet) : (e' y).1 = b :=
   e'.coe_fst (e'.mem_source.2 hb)
 #align trivialization.coe_coe_fst Trivialization.coe_coe_fst
+-/
 
+#print Trivialization.mk_mem_target /-
 theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
   e'.toPretrivialization.mem_target
 #align trivialization.mk_mem_target Trivialization.mk_mem_target
+-/
 
+#print Trivialization.symm_apply_apply /-
 theorem symm_apply_apply {x : TotalSpace E} (hx : x ∈ e'.source) :
     e'.toLocalHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
+-/
 
+#print Trivialization.symm_coe_proj /-
 @[simp, mfld_simps]
 theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π E)) (h : x ∈ e.baseSet) :
     (e.toLocalHomeomorph.symm (x, y)).1 = x :=
   e.proj_symm_apply' h
 #align trivialization.symm_coe_proj Trivialization.symm_coe_proj
+-/
 
 section Zero
 
@@ -595,38 +751,51 @@ protected noncomputable def symm (e : Trivialization F (π E)) (b : B) (y : F) :
 #align trivialization.symm Trivialization.symm
 -/
 
+#print Trivialization.symm_apply /-
 theorem symm_apply (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
+-/
 
+#print Trivialization.symm_apply_of_not_mem /-
 theorem symm_apply_of_not_mem (e : Trivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_mem
+-/
 
+#print Trivialization.mk_symm /-
 theorem mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     totalSpaceMk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
+-/
 
+#print Trivialization.symm_proj_apply /-
 theorem symm_proj_apply (e : Trivialization F (π E)) (z : TotalSpace E) (hz : z.proj ∈ e.baseSet) :
     e.symm z.proj (e z).2 = z.2 :=
   e.toPretrivialization.symm_proj_apply z hz
 #align trivialization.symm_proj_apply Trivialization.symm_proj_apply
+-/
 
+#print Trivialization.symm_apply_apply_mk /-
 theorem symm_apply_apply_mk (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
     e.symm b (e (totalSpaceMk b y)).2 = y :=
   e.symm_proj_apply (totalSpaceMk b y) hb
 #align trivialization.symm_apply_apply_mk Trivialization.symm_apply_apply_mk
+-/
 
+#print Trivialization.apply_mk_symm /-
 theorem apply_mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e (totalSpaceMk b (e.symm b y)) = (b, y) :=
   e.toPretrivialization.apply_mk_symm hb y
 #align trivialization.apply_mk_symm Trivialization.apply_mk_symm
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Trivialization.continuousOn_symm /-
 theorem continuousOn_symm (e : Trivialization F (π E)) :
     ContinuousOn (fun z : B × F => totalSpaceMk z.1 (e.symm z.1 z.2)) (e.baseSet ×ˢ univ) :=
   by
@@ -638,6 +807,7 @@ theorem continuousOn_symm (e : Trivialization F (π E)) :
   rw [← e.target_eq]
   exact e.to_local_homeomorph.continuous_on_symm
 #align trivialization.continuous_on_symm Trivialization.continuousOn_symm
+-/
 
 end Zero
 
@@ -657,11 +827,13 @@ def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization
 #align trivialization.trans_fiber_homeomorph Trivialization.transFiberHomeomorph
 -/
 
+#print Trivialization.transFiberHomeomorph_apply /-
 @[simp]
 theorem transFiberHomeomorph_apply {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') (x : Z) : e.transFiberHomeomorph h x = ((e x).1, h (e x).2) :=
   rfl
 #align trivialization.trans_fiber_homeomorph_apply Trivialization.transFiberHomeomorph_apply
+-/
 
 #print Trivialization.coordChange /-
 /-- Coordinate transformation in the fiber induced by a pair of bundle trivializations. See also
@@ -671,6 +843,7 @@ def coordChange (e₁ e₂ : Trivialization F proj) (b : B) (x : F) : F :=
 #align trivialization.coord_change Trivialization.coordChange
 -/
 
+#print Trivialization.mk_coordChange /-
 theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
     (b, e₁.coordChange e₂ b x) = e₂ (e₁.toLocalHomeomorph.symm (b, x)) :=
@@ -680,21 +853,29 @@ theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈
   · rwa [e₁.proj_symm_apply' h₁]
   · rwa [e₁.proj_symm_apply' h₁]
 #align trivialization.mk_coord_change Trivialization.mk_coordChange
+-/
 
+#print Trivialization.coordChange_apply_snd /-
 theorem coordChange_apply_snd (e₁ e₂ : Trivialization F proj) {p : Z} (h : proj p ∈ e₁.baseSet) :
     e₁.coordChange e₂ (proj p) (e₁ p).snd = (e₂ p).snd := by
   rw [coord_change, e₁.symm_apply_mk_proj (e₁.mem_source.2 h)]
 #align trivialization.coord_change_apply_snd Trivialization.coordChange_apply_snd
+-/
 
+#print Trivialization.coordChange_same_apply /-
 theorem coordChange_same_apply (e : Trivialization F proj) {b : B} (h : b ∈ e.baseSet) (x : F) :
     e.coordChange e b x = x := by rw [coord_change, e.apply_symm_apply' h]
 #align trivialization.coord_change_same_apply Trivialization.coordChange_same_apply
+-/
 
+#print Trivialization.coordChange_same /-
 theorem coordChange_same (e : Trivialization F proj) {b : B} (h : b ∈ e.baseSet) :
     e.coordChange e b = id :=
   funext <| e.coordChange_same_apply h
 #align trivialization.coord_change_same Trivialization.coordChange_same
+-/
 
+#print Trivialization.coordChange_coordChange /-
 theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
     e₂.coordChange e₃ b (e₁.coordChange e₂ b x) = e₁.coordChange e₃ b x :=
@@ -703,7 +884,9 @@ theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B}
     coord_change]
   rwa [e₂.mem_source, e₁.proj_symm_apply' h₁]
 #align trivialization.coord_change_coord_change Trivialization.coordChange_coordChange
+-/
 
+#print Trivialization.continuous_coordChange /-
 theorem continuous_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : Continuous (e₁.coordChange e₂ b) :=
   by
@@ -716,6 +899,7 @@ theorem continuous_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁
   · intro x
     rwa [e₂.mem_source, e₁.proj_symm_apply' h₁]
 #align trivialization.continuous_coord_change Trivialization.continuous_coordChange
+-/
 
 #print Trivialization.coordChangeHomeomorph /-
 /-- Coordinate transformation in the fiber induced by a pair of bundle trivializations,
@@ -732,18 +916,22 @@ protected def coordChangeHomeomorph (e₁ e₂ : Trivialization F proj) {b : B}
 #align trivialization.coord_change_homeomorph Trivialization.coordChangeHomeomorph
 -/
 
+#print Trivialization.coordChangeHomeomorph_coe /-
 @[simp]
 theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : ⇑(e₁.coordChangeHomeomorph e₂ h₁ h₂) = e₁.coordChange e₂ b :=
   rfl
 #align trivialization.coord_change_homeomorph_coe Trivialization.coordChangeHomeomorph_coe
+-/
 
 variable {F} {B' : Type _} [TopologicalSpace B']
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Trivialization.isImage_preimage_prod /-
 theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
     e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
 #align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prod
+-/
 
 #print Trivialization.restrOpen /-
 /-- Restrict a `trivialization` to an open set in the base. `-/
@@ -762,13 +950,16 @@ protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s)
 
 section Piecewise
 
+#print Trivialization.frontier_preimage /-
 theorem frontier_preimage (e : Trivialization F proj) (s : Set B) :
     e.source ∩ frontier (proj ⁻¹' s) = proj ⁻¹' (e.baseSet ∩ frontier s) := by
   rw [← (e.is_image_preimage_prod s).frontier.preimage_eq, frontier_prod_univ_eq,
     (e.is_image_preimage_prod _).preimage_eq, e.source_eq, preimage_inter]
 #align trivialization.frontier_preimage Trivialization.frontier_preimage
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Trivialization.piecewise /-
 /-- Given two bundle trivializations `e`, `e'` of `proj : Z → B` and a set `s : set B` such that
 the base sets of `e` and `e'` intersect `frontier s` on the same set and `e p = e' p` whenever
 `proj p ∈ e.base_set ∩ frontier s`, `e.piecewise e' s Hs Heq` is the bundle trivialization over
@@ -788,7 +979,9 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
   target_eq := by simp [e.target_eq, e'.target_eq, prod_univ]
   proj_toFun := by rintro p (⟨he, hs⟩ | ⟨he, hs⟩) <;> simp [*]
 #align trivialization.piecewise Trivialization.piecewise
+-/
 
+#print Trivialization.piecewiseLeOfEq /-
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B`
 over a linearly ordered base `B` and a point `a ∈ e.base_set ∩ e'.base_set` such that
 `e` equals `e'` on `proj ⁻¹' {a}`, `e.piecewise_le_of_eq e' a He He' Heq` is the bundle
@@ -803,6 +996,7 @@ noncomputable def piecewiseLeOfEq [LinearOrder B] [OrderTopology B] (e e' : Triv
         simp [He, He', mem_singleton_iff.1 (frontier_Iic_subset _ hx)])
     fun p hp => Heq p <| frontier_Iic_subset _ hp.2
 #align trivialization.piecewise_le_of_eq Trivialization.piecewiseLeOfEq
+-/
 
 #print Trivialization.piecewiseLe /-
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B` over a
@@ -822,6 +1016,7 @@ noncomputable def piecewiseLe [LinearOrder B] [OrderTopology B] (e e' : Triviali
 #align trivialization.piecewise_le Trivialization.piecewiseLe
 -/
 
+#print Trivialization.disjointUnion /-
 /-- Given two bundle trivializations `e`, `e'` over disjoint sets, `e.disjoint_union e' H` is the
 bundle trivialization over the union of the base sets that agrees with `e` and `e'` over their
 base sets. -/
@@ -847,6 +1042,7 @@ noncomputable def disjointUnion (e e' : Trivialization F proj) (H : Disjoint e.b
       simp only [e.source_eq, e'.source_eq] at hp' ⊢
       exact fun h => H.le_bot ⟨h, hp'⟩
 #align trivialization.disjoint_union Trivialization.disjointUnion
+-/
 
 end Piecewise

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -131,7 +131,7 @@ theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEquiv.symm x) = x.1 :=
   by
   have := (e.coe_fst (e.to_local_equiv.map_target hx)).symm
-  rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this
+  rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this 
 #align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_apply
 
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
@@ -844,7 +844,7 @@ noncomputable def disjointUnion (e e' : Trivialization F proj) (H : Disjoint e.b
       rw [piecewise_eq_of_mem, e.coe_fst] <;> exact hp
     · show (e.source.piecewise e e' p).1 = proj p
       rw [piecewise_eq_of_not_mem, e'.coe_fst hp']
-      simp only [e.source_eq, e'.source_eq] at hp'⊢
+      simp only [e.source_eq, e'.source_eq] at hp' ⊢
       exact fun h => H.le_bot ⟨h, hp'⟩
 #align trivialization.disjoint_union Trivialization.disjointUnion

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -58,7 +58,7 @@ type of linear trivializations is not even particularly well-behaved.
 
 open TopologicalSpace Filter Set Bundle
 
-open Topology Classical Bundle
+open scoped Topology Classical Bundle
 
 variable {ι : Type _} {B : Type _} {F : Type _} {E : B → Type _}

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -89,72 +89,30 @@ instance : CoeFun (Pretrivialization F proj) fun _ => Z → B × F :=
 
 variable {F} (e : Pretrivialization F proj) {x : Z}
 
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 @[simp, mfld_simps]
 theorem coe_coe : ⇑e.toLocalEquiv = e :=
   rfl
 #align pretrivialization.coe_coe Pretrivialization.coe_coe
 
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 @[simp, mfld_simps]
 theorem coe_fst (ex : x ∈ e.source) : (e x).1 = proj x :=
   e.proj_toFun x ex
 #align pretrivialization.coe_fst Pretrivialization.coe_fst
 
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 theorem mem_source : x ∈ e.source ↔ proj x ∈ e.baseSet := by rw [e.source_eq, mem_preimage]
 #align pretrivialization.mem_source Pretrivialization.mem_source
 
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 theorem coe_fst' (ex : proj x ∈ e.baseSet) : (e x).1 = proj x :=
   e.coe_fst (e.mem_source.2 ex)
 #align pretrivialization.coe_fst' Pretrivialization.coe_fst'
 
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 protected theorem eqOn : EqOn (Prod.fst ∘ e) proj e.source := fun x hx => e.coe_fst hx
 #align pretrivialization.eq_on Pretrivialization.eqOn
 
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 theorem mk_proj_snd (ex : x ∈ e.source) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst ex).symm rfl
 #align pretrivialization.mk_proj_snd Pretrivialization.mk_proj_snd
 
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 theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst' ex).symm rfl
 #align pretrivialization.mk_proj_snd' Pretrivialization.mk_proj_snd'
@@ -166,100 +124,46 @@ def setSymm : e.target → Z :=
 #align pretrivialization.set_symm Pretrivialization.setSymm
 -/
 
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 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
   rw [e.target_eq, prod_univ, mem_preimage]
 #align pretrivialization.mem_target Pretrivialization.mem_target
 
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 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEquiv.symm x) = x.1 :=
   by
   have := (e.coe_fst (e.to_local_equiv.map_target hx)).symm
   rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this
 #align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_apply
 
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 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     proj (e.toLocalEquiv.symm (b, x)) = b :=
   e.proj_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.proj_symm_apply' Pretrivialization.proj_symm_apply'
 
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 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet := fun b hb =>
   let ⟨y⟩ := ‹Nonempty F›
   ⟨e.toLocalEquiv.symm (b, y), e.toLocalEquiv.map_target <| e.mem_target.2 hb,
     e.proj_symm_apply' hb⟩
 #align pretrivialization.proj_surj_on_base_set Pretrivialization.proj_surjOn_baseSet
 
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 theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalEquiv.symm x) = x :=
   e.toLocalEquiv.right_inv hx
 #align pretrivialization.apply_symm_apply Pretrivialization.apply_symm_apply
 
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 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     e (e.toLocalEquiv.symm (b, x)) = (b, x) :=
   e.apply_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.apply_symm_apply' Pretrivialization.apply_symm_apply'
 
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 theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toLocalEquiv.symm (e x) = x :=
   e.toLocalEquiv.left_inv hx
 #align pretrivialization.symm_apply_apply Pretrivialization.symm_apply_apply
 
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 @[simp, mfld_simps]
 theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
     e.toLocalEquiv.symm (proj x, (e x).2) = x := by
   rw [← e.coe_fst ex, Prod.mk.eta, ← e.coe_coe, e.to_local_equiv.left_inv ex]
 #align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_proj
 
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 @[simp, mfld_simps]
 theorem preimage_symm_proj_baseSet :
     e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target :=
@@ -269,12 +173,6 @@ theorem preimage_symm_proj_baseSet :
   exact e.mem_target.mp hx
 #align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSet
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, mfld_simps]
@@ -288,47 +186,23 @@ theorem preimage_symm_proj_inter (s : Set B) :
   rw [e.proj_symm_apply' h]
 #align pretrivialization.preimage_symm_proj_inter Pretrivialization.preimage_symm_proj_inter
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem target_inter_preimage_symm_source_eq (e f : Pretrivialization F proj) :
     f.target ∩ f.toLocalEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [inter_comm, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]
 #align pretrivialization.target_inter_preimage_symm_source_eq Pretrivialization.target_inter_preimage_symm_source_eq
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem trans_source (e f : Pretrivialization F proj) :
     (f.toLocalEquiv.symm.trans e.toLocalEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [LocalEquiv.trans_source, LocalEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
 #align pretrivialization.trans_source Pretrivialization.trans_source
 
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 theorem symm_trans_symm (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm = e'.toLocalEquiv.symm.trans e.toLocalEquiv :=
   by rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
 #align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symm
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
@@ -336,12 +210,6 @@ theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
     e.preimage_symm_proj_inter, inter_comm]
 #align pretrivialization.symm_trans_source_eq Pretrivialization.symm_trans_source_eq
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
@@ -350,43 +218,19 @@ theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
 
 variable {B F} (e' : Pretrivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
 
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 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align pretrivialization.coe_mem_source Pretrivialization.coe_mem_source
 
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 @[simp, mfld_simps]
 theorem coe_coe_fst (hb : b ∈ e'.baseSet) : (e' y).1 = b :=
   e'.coe_fst (e'.mem_source.2 hb)
 #align pretrivialization.coe_coe_fst Pretrivialization.coe_coe_fst
 
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 theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSet :=
   e'.mem_target
 #align pretrivialization.mk_mem_target Pretrivialization.mk_mem_target
 
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 theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π E)) (h : x ∈ e'.baseSet) :
     (e'.toLocalEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
@@ -406,78 +250,36 @@ protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F
 #align pretrivialization.symm Pretrivialization.symm
 -/
 
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 theorem symm_apply (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
 
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 theorem symm_apply_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align pretrivialization.symm_apply_of_not_mem Pretrivialization.symm_apply_of_not_mem
 
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 theorem coe_symm_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) :
     (e.symm b : F → E b) = 0 :=
   funext fun y => dif_neg hb
 #align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_mem
 
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 theorem mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     totalSpaceMk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
   rw [e.symm_apply hb, total_space.mk_cast, total_space.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
 
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 theorem symm_proj_apply (e : Pretrivialization F (π E)) (z : TotalSpace E)
     (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 := by
   rw [e.symm_apply hz, cast_eq_iff_heq, e.mk_proj_snd' hz, e.symm_apply_apply (e.mem_source.mpr hz)]
 #align pretrivialization.symm_proj_apply Pretrivialization.symm_proj_apply
 
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 theorem symm_apply_apply_mk (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
     e.symm b (e (totalSpaceMk b y)).2 = y :=
   e.symm_proj_apply (totalSpaceMk b y) hb
 #align pretrivialization.symm_apply_apply_mk Pretrivialization.symm_apply_apply_mk
 
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 theorem apply_mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e (totalSpaceMk b (e.symm b y)) = (b, y) := by
   rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
@@ -522,12 +324,6 @@ instance : CoeFun (Trivialization F proj) fun _ => Z → B × F :=
 instance : Coe (Trivialization F proj) (Pretrivialization F proj) :=
   ⟨toPretrivialization⟩
 
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 theorem toPretrivialization_injective :
     Function.Injective fun e : Trivialization F proj => e.toPretrivialization :=
   by
@@ -537,250 +333,109 @@ theorem toPretrivialization_injective :
   exact id
 #align trivialization.to_pretrivialization_injective Trivialization.toPretrivialization_injective
 
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 @[simp, mfld_simps]
 theorem coe_coe : ⇑e.toLocalHomeomorph = e :=
   rfl
 #align trivialization.coe_coe Trivialization.coe_coe
 
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 @[simp, mfld_simps]
 theorem coe_fst (ex : x ∈ e.source) : (e x).1 = proj x :=
   e.proj_toFun x ex
 #align trivialization.coe_fst Trivialization.coe_fst
 
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 protected theorem eqOn : EqOn (Prod.fst ∘ e) proj e.source := fun x hx => e.coe_fst hx
 #align trivialization.eq_on Trivialization.eqOn
 
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 theorem mem_source : x ∈ e.source ↔ proj x ∈ e.baseSet := by rw [e.source_eq, mem_preimage]
 #align trivialization.mem_source Trivialization.mem_source
 
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 theorem coe_fst' (ex : proj x ∈ e.baseSet) : (e x).1 = proj x :=
   e.coe_fst (e.mem_source.2 ex)
 #align trivialization.coe_fst' Trivialization.coe_fst'
 
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 theorem mk_proj_snd (ex : x ∈ e.source) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst ex).symm rfl
 #align trivialization.mk_proj_snd Trivialization.mk_proj_snd
 
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 theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst' ex).symm rfl
 #align trivialization.mk_proj_snd' Trivialization.mk_proj_snd'
 
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 theorem source_inter_preimage_target_inter (s : Set (B × F)) :
     e.source ∩ e ⁻¹' (e.target ∩ s) = e.source ∩ e ⁻¹' s :=
   e.toLocalHomeomorph.source_inter_preimage_target_inter s
 #align trivialization.source_inter_preimage_target_inter Trivialization.source_inter_preimage_target_inter
 
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 @[simp, mfld_simps]
 theorem coe_mk (e : LocalHomeomorph Z (B × F)) (i j k l m) (x : Z) :
     (Trivialization.mk e i j k l m : Trivialization F proj) x = e x :=
   rfl
 #align trivialization.coe_mk Trivialization.coe_mk
 
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 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet :=
   e.toPretrivialization.mem_target
 #align trivialization.mem_target Trivialization.mem_target
 
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 theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toLocalHomeomorph.symm x ∈ e.source :=
   e.toLocalHomeomorph.map_target hx
 #align trivialization.map_target Trivialization.map_target
 
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 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalHomeomorph.symm x) = x.1 :=
   e.toPretrivialization.proj_symm_apply hx
 #align trivialization.proj_symm_apply Trivialization.proj_symm_apply
 
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 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     proj (e.toLocalHomeomorph.symm (b, x)) = b :=
   e.toPretrivialization.proj_symm_apply' hx
 #align trivialization.proj_symm_apply' Trivialization.proj_symm_apply'
 
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 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet :=
   e.toPretrivialization.proj_surjOn_baseSet
 #align trivialization.proj_surj_on_base_set Trivialization.proj_surjOn_baseSet
 
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 theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalHomeomorph.symm x) = x :=
   e.toLocalHomeomorph.right_inv hx
 #align trivialization.apply_symm_apply Trivialization.apply_symm_apply
 
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 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     e (e.toLocalHomeomorph.symm (b, x)) = (b, x) :=
   e.toPretrivialization.apply_symm_apply' hx
 #align trivialization.apply_symm_apply' Trivialization.apply_symm_apply'
 
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 @[simp, mfld_simps]
 theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toLocalHomeomorph.symm (proj x, (e x).2) = x :=
   e.toPretrivialization.symm_apply_mk_proj ex
 #align trivialization.symm_apply_mk_proj Trivialization.symm_apply_mk_proj
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_source_eq (e e' : Trivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_source_eq e.toPretrivialization e'
 #align trivialization.symm_trans_source_eq Trivialization.symm_trans_source_eq
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_target_eq (e e' : Trivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_target_eq e.toPretrivialization e'
 #align trivialization.symm_trans_target_eq Trivialization.symm_trans_target_eq
 
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 theorem coe_fst_eventuallyEq_proj (ex : x ∈ e.source) : Prod.fst ∘ e =ᶠ[𝓝 x] proj :=
   mem_nhds_iff.2 ⟨e.source, fun y hy => e.coe_fst hy, e.open_source, ex⟩
 #align trivialization.coe_fst_eventually_eq_proj Trivialization.coe_fst_eventuallyEq_proj
 
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 theorem coe_fst_eventuallyEq_proj' (ex : proj x ∈ e.baseSet) : Prod.fst ∘ e =ᶠ[𝓝 x] proj :=
   e.coe_fst_eventuallyEq_proj (e.mem_source.2 ex)
 #align trivialization.coe_fst_eventually_eq_proj' Trivialization.coe_fst_eventuallyEq_proj'
 
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 theorem map_proj_nhds (ex : x ∈ e.source) : map proj (𝓝 x) = 𝓝 (proj x) := by
   rw [← e.coe_fst ex, ← map_congr (e.coe_fst_eventually_eq_proj ex), ← map_map, ← e.coe_coe,
     e.to_local_homeomorph.map_nhds_eq ex, map_fst_nhds]
 #align trivialization.map_proj_nhds Trivialization.map_proj_nhds
 
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 theorem preimage_subset_source {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ⊆ e.source :=
   fun p hp => e.mem_source.mpr (hb hp)
 #align trivialization.preimage_subset_source Trivialization.preimage_subset_source
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     e '' (proj ⁻¹' s) = s ×ˢ univ :=
@@ -792,12 +447,6 @@ theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     ⟨e.invFun p, mem_preimage.mpr ((e.proj_symm_apply hp').symm ▸ hp.1), e.apply_symm_apply hp'⟩
 #align trivialization.image_preimage_eq_prod_univ Trivialization.image_preimage_eq_prod_univ
 
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 /-- The preimage of a subset of the base set is homeomorphic to the product with the fiber. -/
 def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ s × F :=
   (e.toLocalHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
@@ -805,47 +454,29 @@ def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ
     ((Homeomorph.Set.prod s univ).trans ((Homeomorph.refl s).prodCongr (Homeomorph.Set.univ F)))
 #align trivialization.preimage_homeomorph Trivialization.preimageHomeomorph
 
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 @[simp]
 theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj ⁻¹' s) :
     e.preimageHomeomorph hb p = (⟨proj p, p.2⟩, (e p).2) :=
   Prod.ext (Subtype.ext (e.proj_toFun p (e.mem_source.mpr (hb p.2)))) rfl
 #align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_apply
 
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 @[simp]
 theorem preimageHomeomorph_symm_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : s × F) :
     (e.preimageHomeomorph hb).symm p = ⟨e.symm (p.1, p.2), ((e.preimageHomeomorph hb).symm p).2⟩ :=
   rfl
 #align trivialization.preimage_homeomorph_symm_apply Trivialization.preimageHomeomorph_symm_apply
 
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 /-- The source is homeomorphic to the product of the base set with the fiber. -/
 def sourceHomeomorphBaseSetProd : e.source ≃ₜ e.baseSet × F :=
   (Homeomorph.setCongr e.source_eq).trans (e.preimageHomeomorph subset_rfl)
 #align trivialization.source_homeomorph_base_set_prod Trivialization.sourceHomeomorphBaseSetProd
 
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 @[simp]
 theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
     e.sourceHomeomorphBaseSetProd p = (⟨proj p, e.mem_source.mp p.2⟩, (e p).2) :=
   e.preimageHomeomorph_apply subset_rfl ⟨p, e.mem_source.mp p.2⟩
 #align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_apply
 
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 @[simp]
 theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
     e.sourceHomeomorphBaseSetProd.symm p =
@@ -853,12 +484,6 @@ theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
   rfl
 #align trivialization.source_homeomorph_base_set_prod_symm_apply Trivialization.sourceHomeomorphBaseSetProd_symm_apply
 
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 /-- Each fiber of a trivialization is homeomorphic to the specified fiber. -/
 def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b} ≃ₜ F :=
   (e.preimageHomeomorph (Set.singleton_subset_iff.mpr hb)).trans
@@ -866,18 +491,12 @@ def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b}
       (Homeomorph.punitProd F))
 #align trivialization.preimage_singleton_homeomorph Trivialization.preimageSingletonHomeomorph
 
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 @[simp]
 theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : proj ⁻¹' {b}) :
     e.preimageSingletonHomeomorph hb p = (e p).2 :=
   rfl
 #align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_apply
 
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 @[simp]
 theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p : F) :
     (e.preimageSingletonHomeomorph hb).symm p =
@@ -885,23 +504,11 @@ theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p
   rfl
 #align trivialization.preimage_singleton_homeomorph_symm_apply Trivialization.preimageSingletonHomeomorph_symm_apply
 
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 /-- In the domain of a bundle trivialization, the projection is continuous-/
 theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
   (e.map_proj_nhds ex).le
 #align trivialization.continuous_at_proj Trivialization.continuousAt_proj
 
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 /-- Composition of a `trivialization` and a `homeomorph`. -/
 protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
     Trivialization F (proj ∘ h)
@@ -916,12 +523,6 @@ protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ
     simp [hp]
 #align trivialization.comp_homeomorph Trivialization.compHomeomorph
 
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 /-- Read off the continuity of a function `f : Z → X` at `z : Z` by transferring via a
 trivialization of `Z` containing `z`. -/
 theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z → X} {z : Z}
@@ -936,12 +537,6 @@ theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z →
     LocalHomeomorph.symm_symm]
 #align trivialization.continuous_at_of_comp_right Trivialization.continuousAt_of_comp_right
 
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 /-- Read off the continuity of a function `f : X → Z` at `x : X` by transferring via a
 trivialization of `Z` containing `f x`. -/
 theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z} {x : X}
@@ -956,74 +551,32 @@ theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z
 
 variable {E} (e' : Trivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
 
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 protected theorem continuousOn : ContinuousOn e' e'.source :=
   e'.continuous_toFun
 #align trivialization.continuous_on Trivialization.continuousOn
 
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 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align trivialization.coe_mem_source Trivialization.coe_mem_source
 
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 theorem open_target' : IsOpen e'.target := by rw [e'.target_eq];
   exact e'.open_base_set.prod isOpen_univ
 #align trivialization.open_target Trivialization.open_target'
 
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 @[simp, mfld_simps]
 theorem coe_coe_fst (hb : b ∈ e'.baseSet) : (e' y).1 = b :=
   e'.coe_fst (e'.mem_source.2 hb)
 #align trivialization.coe_coe_fst Trivialization.coe_coe_fst
 
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 theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
   e'.toPretrivialization.mem_target
 #align trivialization.mk_mem_target Trivialization.mk_mem_target
 
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 theorem symm_apply_apply {x : TotalSpace E} (hx : x ∈ e'.source) :
     e'.toLocalHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 
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 @[simp, mfld_simps]
 theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π E)) (h : x ∈ e.baseSet) :
     (e.toLocalHomeomorph.symm (x, y)).1 = x :=
@@ -1042,78 +595,36 @@ protected noncomputable def symm (e : Trivialization F (π E)) (b : B) (y : F) :
 #align trivialization.symm Trivialization.symm
 -/
 
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 theorem symm_apply (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
 
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 theorem symm_apply_of_not_mem (e : Trivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_mem
 
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 theorem mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     totalSpaceMk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
 
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 theorem symm_proj_apply (e : Trivialization F (π E)) (z : TotalSpace E) (hz : z.proj ∈ e.baseSet) :
     e.symm z.proj (e z).2 = z.2 :=
   e.toPretrivialization.symm_proj_apply z hz
 #align trivialization.symm_proj_apply Trivialization.symm_proj_apply
 
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 theorem symm_apply_apply_mk (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
     e.symm b (e (totalSpaceMk b y)).2 = y :=
   e.symm_proj_apply (totalSpaceMk b y) hb
 #align trivialization.symm_apply_apply_mk Trivialization.symm_apply_apply_mk
 
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 theorem apply_mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e (totalSpaceMk b (e.symm b y)) = (b, y) :=
   e.toPretrivialization.apply_mk_symm hb y
 #align trivialization.apply_mk_symm Trivialization.apply_mk_symm
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem continuousOn_symm (e : Trivialization F (π E)) :
@@ -1146,12 +657,6 @@ def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization
 #align trivialization.trans_fiber_homeomorph Trivialization.transFiberHomeomorph
 -/
 
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 @[simp]
 theorem transFiberHomeomorph_apply {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') (x : Z) : e.transFiberHomeomorph h x = ((e x).1, h (e x).2) :=
@@ -1166,12 +671,6 @@ def coordChange (e₁ e₂ : Trivialization F proj) (b : B) (x : F) : F :=
 #align trivialization.coord_change Trivialization.coordChange
 -/
 
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 theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
     (b, e₁.coordChange e₂ b x) = e₂ (e₁.toLocalHomeomorph.symm (b, x)) :=
@@ -1182,44 +681,20 @@ theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈
   · rwa [e₁.proj_symm_apply' h₁]
 #align trivialization.mk_coord_change Trivialization.mk_coordChange
 
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 theorem coordChange_apply_snd (e₁ e₂ : Trivialization F proj) {p : Z} (h : proj p ∈ e₁.baseSet) :
     e₁.coordChange e₂ (proj p) (e₁ p).snd = (e₂ p).snd := by
   rw [coord_change, e₁.symm_apply_mk_proj (e₁.mem_source.2 h)]
 #align trivialization.coord_change_apply_snd Trivialization.coordChange_apply_snd
 
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 theorem coordChange_same_apply (e : Trivialization F proj) {b : B} (h : b ∈ e.baseSet) (x : F) :
     e.coordChange e b x = x := by rw [coord_change, e.apply_symm_apply' h]
 #align trivialization.coord_change_same_apply Trivialization.coordChange_same_apply
 
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 theorem coordChange_same (e : Trivialization F proj) {b : B} (h : b ∈ e.baseSet) :
     e.coordChange e b = id :=
   funext <| e.coordChange_same_apply h
 #align trivialization.coord_change_same Trivialization.coordChange_same
 
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 theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
     e₂.coordChange e₃ b (e₁.coordChange e₂ b x) = e₁.coordChange e₃ b x :=
@@ -1229,12 +704,6 @@ theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B}
   rwa [e₂.mem_source, e₁.proj_symm_apply' h₁]
 #align trivialization.coord_change_coord_change Trivialization.coordChange_coordChange
 
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 theorem continuous_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : Continuous (e₁.coordChange e₂ b) :=
   by
@@ -1263,12 +732,6 @@ protected def coordChangeHomeomorph (e₁ e₂ : Trivialization F proj) {b : B}
 #align trivialization.coord_change_homeomorph Trivialization.coordChangeHomeomorph
 -/
 
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 @[simp]
 theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : ⇑(e₁.coordChangeHomeomorph e₂ h₁ h₂) = e₁.coordChange e₂ b :=
@@ -1277,12 +740,6 @@ theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h
 
 variable {F} {B' : Type _} [TopologicalSpace B']
 
-/- warning: trivialization.is_image_preimage_prod -> Trivialization.isImage_preimage_prod is a dubious translation:
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-  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (s : Set.{u1} B), LocalHomeomorph.IsImage.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e) (Set.preimage.{u3, u1} Z B proj s) (Set.prod.{u1, u2} B F s (Set.univ.{u2} F))
-but is expected to have type
-  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (s : Set.{u3} B), LocalHomeomorph.IsImage.{u1, max u3 u2} Z (Prod.{u3, u2} B F) _inst_3 (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e) (Set.preimage.{u1, u3} Z B proj s) (Set.prod.{u3, u2} B F s (Set.univ.{u2} F))
-Case conversion may be inaccurate. Consider using '#align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
     e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
@@ -1305,24 +762,12 @@ protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s)
 
 section Piecewise
 
-/- warning: trivialization.frontier_preimage -> Trivialization.frontier_preimage is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align trivialization.frontier_preimage Trivialization.frontier_preimageₓ'. -/
 theorem frontier_preimage (e : Trivialization F proj) (s : Set B) :
     e.source ∩ frontier (proj ⁻¹' s) = proj ⁻¹' (e.baseSet ∩ frontier s) := by
   rw [← (e.is_image_preimage_prod s).frontier.preimage_eq, frontier_prod_univ_eq,
     (e.is_image_preimage_prod _).preimage_eq, e.source_eq, preimage_inter]
 #align trivialization.frontier_preimage Trivialization.frontier_preimage
 
-/- warning: trivialization.piecewise -> Trivialization.piecewise is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align trivialization.piecewise Trivialization.piecewiseₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Given two bundle trivializations `e`, `e'` of `proj : Z → B` and a set `s : set B` such that
 the base sets of `e` and `e'` intersect `frontier s` on the same set and `e p = e' p` whenever
@@ -1344,9 +789,6 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
   proj_toFun := by rintro p (⟨he, hs⟩ | ⟨he, hs⟩) <;> simp [*]
 #align trivialization.piecewise Trivialization.piecewise
 
-/- warning: trivialization.piecewise_le_of_eq -> Trivialization.piecewiseLeOfEq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align trivialization.piecewise_le_of_eq Trivialization.piecewiseLeOfEqₓ'. -/
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B`
 over a linearly ordered base `B` and a point `a ∈ e.base_set ∩ e'.base_set` such that
 `e` equals `e'` on `proj ⁻¹' {a}`, `e.piecewise_le_of_eq e' a He He' Heq` is the bundle
@@ -1380,12 +822,6 @@ noncomputable def piecewiseLe [LinearOrder B] [OrderTopology B] (e e' : Triviali
 #align trivialization.piecewise_le Trivialization.piecewiseLe
 -/
 
-/- warning: trivialization.disjoint_union -> Trivialization.disjointUnion is a dubious translation:
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-  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e' : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj), (Disjoint.{u1} (Set.{u1} B) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} B) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} B) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} B) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} B) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} B) (Set.completeBooleanAlgebra.{u1} B)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} B) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} B) (Set.booleanAlgebra.{u1} B))) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e')) -> (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj)
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-Case conversion may be inaccurate. Consider using '#align trivialization.disjoint_union Trivialization.disjointUnionₓ'. -/
 /-- Given two bundle trivializations `e`, `e'` over disjoint sets, `e.disjoint_union e' H` is the
 bundle trivialization over the union of the base sets that agrees with `e` and `e'` over their
 base sets. -/

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -531,7 +531,7 @@ Case conversion may be inaccurate. Consider using '#align trivialization.to_pret
 theorem toPretrivialization_injective :
     Function.Injective fun e : Trivialization F proj => e.toPretrivialization :=
   by
-  intro e e'
+  intro e e';
   rw [Pretrivialization.ext_iff, Trivialization.ext_iff, ←
     local_homeomorph.to_local_equiv_injective.eq_iff]
   exact id
@@ -982,9 +982,7 @@ lean 3 declaration is
 but is expected to have type
   forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] (e' : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)), IsOpen.{max u3 u2} (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (LocalEquiv.target.{max u3 u1, max u3 u2} (Bundle.TotalSpace.{u3, u1} B E) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u1, max u3 u2} (Bundle.TotalSpace.{u3, u1} B E) (Prod.{u3, u2} B F) _inst_4 (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e')))
 Case conversion may be inaccurate. Consider using '#align trivialization.open_target Trivialization.open_target'ₓ'. -/
-theorem open_target' : IsOpen e'.target :=
-  by
-  rw [e'.target_eq]
+theorem open_target' : IsOpen e'.target := by rw [e'.target_eq];
   exact e'.open_base_set.prod isOpen_univ
 #align trivialization.open_target Trivialization.open_target'
 
@@ -1124,9 +1122,7 @@ theorem continuousOn_symm (e : Trivialization F (π E)) :
   have :
     ∀ (z : B × F) (hz : z ∈ e.base_set ×ˢ (univ : Set F)),
       total_space_mk z.1 (e.symm z.1 z.2) = e.to_local_homeomorph.symm z :=
-    by
-    rintro x ⟨hx : x.1 ∈ e.base_set, _⟩
-    simp_rw [e.mk_symm hx, Prod.mk.eta]
+    by rintro x ⟨hx : x.1 ∈ e.base_set, _⟩; simp_rw [e.mk_symm hx, Prod.mk.eta]
   refine' ContinuousOn.congr _ this
   rw [← e.target_eq]
   exact e.to_local_homeomorph.continuous_on_symm
@@ -1398,13 +1394,10 @@ noncomputable def disjointUnion (e e' : Trivialization F proj) (H : Disjoint e.b
     where
   toLocalHomeomorph :=
     e.toLocalHomeomorph.disjointUnion e'.toLocalHomeomorph
-      (by
-        rw [e.source_eq, e'.source_eq]
-        exact H.preimage _)
+      (by rw [e.source_eq, e'.source_eq]; exact H.preimage _)
       (by
         rw [e.target_eq, e'.target_eq, disjoint_iff_inf_le]
-        intro x hx
-        exact H.le_bot ⟨hx.1.1, hx.2.1⟩)
+        intro x hx; exact H.le_bot ⟨hx.1.1, hx.2.1⟩)
   baseSet := e.baseSet ∪ e'.baseSet
   open_baseSet := IsOpen.union e.open_baseSet e'.open_baseSet
   source_eq := congr_arg₂ (· ∪ ·) e.source_eq e'.source_eq

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -619,10 +619,7 @@ theorem source_inter_preimage_target_inter (s : Set (B × F)) :
 #align trivialization.source_inter_preimage_target_inter Trivialization.source_inter_preimage_target_inter
 
 /- warning: trivialization.coe_mk -> Trivialization.coe_mk is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align trivialization.coe_mk Trivialization.coe_mkₓ'. -/
 @[simp, mfld_simps]
 theorem coe_mk (e : LocalHomeomorph Z (B × F)) (i j k l m) (x : Z) :
@@ -809,10 +806,7 @@ def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ
 #align trivialization.preimage_homeomorph Trivialization.preimageHomeomorph
 
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 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_applyₓ'. -/
 @[simp]
 theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj ⁻¹' s) :
@@ -821,10 +815,7 @@ theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj 
 #align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_apply
 
 /- warning: trivialization.preimage_homeomorph_symm_apply -> Trivialization.preimageHomeomorph_symm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph_symm_apply Trivialization.preimageHomeomorph_symm_applyₓ'. -/
 @[simp]
 theorem preimageHomeomorph_symm_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : s × F) :
@@ -844,10 +835,7 @@ def sourceHomeomorphBaseSetProd : e.source ≃ₜ e.baseSet × F :=
 #align trivialization.source_homeomorph_base_set_prod Trivialization.sourceHomeomorphBaseSetProd
 
 /- warning: trivialization.source_homeomorph_base_set_prod_apply -> Trivialization.sourceHomeomorphBaseSetProd_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_applyₓ'. -/
 @[simp]
 theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
@@ -856,10 +844,7 @@ theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
 #align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_apply
 
 /- warning: trivialization.source_homeomorph_base_set_prod_symm_apply -> Trivialization.sourceHomeomorphBaseSetProd_symm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod_symm_apply Trivialization.sourceHomeomorphBaseSetProd_symm_applyₓ'. -/
 @[simp]
 theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
@@ -882,10 +867,7 @@ def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b}
 #align trivialization.preimage_singleton_homeomorph Trivialization.preimageSingletonHomeomorph
 
 /- warning: trivialization.preimage_singleton_homeomorph_apply -> Trivialization.preimageSingletonHomeomorph_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_applyₓ'. -/
 @[simp]
 theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : proj ⁻¹' {b}) :
@@ -894,10 +876,7 @@ theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : pr
 #align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_apply
 
 /- warning: trivialization.preimage_singleton_homeomorph_symm_apply -> Trivialization.preimageSingletonHomeomorph_symm_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph_symm_apply Trivialization.preimageSingletonHomeomorph_symm_applyₓ'. -/
 @[simp]
 theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p : F) :
@@ -1370,10 +1349,7 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
 #align trivialization.piecewise Trivialization.piecewise
 
 /- warning: trivialization.piecewise_le_of_eq -> Trivialization.piecewiseLeOfEq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.piecewise_le_of_eq Trivialization.piecewiseLeOfEqₓ'. -/
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B`
 over a linearly ordered base `B` and a point `a ∈ e.base_set ∩ e'.base_set` such that

bump to nightly-2023-03-16-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

d225db81

Diff

@@ -812,7 +812,7 @@ def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ
 lean 3 declaration is
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 but is expected to have type
-  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u3} B} (hb : HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) s (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) => Prod.{u3, u2} (Set.Elem.{u3} B s) F) p) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (Homeomorph.{u1, max u2 u3} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (fun (_x : Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) => Prod.{u3, u2} (Set.Elem.{u3} B s) F) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (Homeomorph.{u1, max u2 u3} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (Homeomorph.{u1, max u2 u3} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (Homeomorph.instEquivLikeHomeomorph.{u1, max u3 u2} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)))) (Trivialization.preimageHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e s hb) p) (Prod.mk.{u3, u2} (Set.Elem.{u3} B s) F (Subtype.mk.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) (proj (Subtype.val.{succ u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) p)) (Subtype.property.{succ u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) p)) (Prod.snd.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e (Subtype.val.{succ u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) p))))
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u3} B} (hb : HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) s (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (FunLike.coe.{max (succ u1) (succ (max u3 u2)), succ u1, succ (max u3 u2)} (Homeomorph.{u1, max u3 u2} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (fun (_x : Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) => Prod.{u3, u2} (Set.Elem.{u3} B s) F) (EmbeddingLike.toFunLike.{max (succ u1) (succ (max u3 u2)), succ u1, succ (max u3 u2)} (Homeomorph.{u1, max u3 u2} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (EquivLike.toEmbeddingLike.{max (succ u1) (succ (max u3 u2)), succ u1, succ (max u3 u2)} (Homeomorph.{u1, max u3 u2} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (Homeomorph.instEquivLikeHomeomorph.{u1, max u3 u2} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2)))) (Trivialization.preimageHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e s hb) p) (Prod.mk.{u3, u2} (Set.Elem.{u3} B s) F (Subtype.mk.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) (proj (Subtype.val.{succ u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) p)) (Subtype.property.{succ u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) p)) (Prod.snd.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e (Subtype.val.{succ u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z (Set.{u1} Z) (Set.instMembershipSet.{u1} Z) x (Set.preimage.{u1, u3} Z B proj s)) p))))
 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_applyₓ'. -/
 @[simp]
 theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj ⁻¹' s) :
@@ -824,7 +824,7 @@ theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj 
 lean 3 declaration is
   forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u1} B} (hb : HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) s (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : Prod.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} (Set.hasCoeToSort.{u1} B) s) F), Eq.{succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} Z) Type.{u3} (Set.hasCoeToSort.{u3} Z) (Set.preimage.{u3, u1} Z B proj s)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (Homeomorph.{max u1 u2, u3} (Prod.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} (Set.hasCoeToSort.{u1} B) s) F) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} Z) Type.{u3} (Set.hasCoeToSort.{u3} Z) (Set.preimage.{u3, u1} Z B proj s)) 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 but is expected to have type
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+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u3} B} (hb : HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) s (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : Prod.{u3, u2} (Set.Elem.{u3} B s) F), Eq.{succ u1} (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (FunLike.coe.{max (succ (max u3 u2)) (succ u1), succ (max u3 u2), succ u1} (Homeomorph.{max u3 u2, u1} (Prod.{u3, u2} (Set.Elem.{u3} B s) F) (Set.Elem.{u1} Z (Set.preimage.{u1, u3} Z B proj s)) (instTopologicalSpaceProd.{u3, u2} (Set.Elem.{u3} B s) F (instTopologicalSpaceSubtype.{u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x s) _inst_1) _inst_2) (instTopologicalSpaceSubtype.{u1} Z (fun (x : Z) => Membership.mem.{u1, u1} Z 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 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph_symm_apply Trivialization.preimageHomeomorph_symm_applyₓ'. -/
 @[simp]
 theorem preimageHomeomorph_symm_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : s × F) :
@@ -847,7 +847,7 @@ def sourceHomeomorphBaseSetProd : e.source ≃ₜ e.baseSet × F :=
 lean 3 declaration is
   forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (p : coeSort.{succ u3, succ (succ u3)} (Set.{u3} Z) Type.{u3} (Set.hasCoeToSort.{u3} Z) (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)))), Eq.{max (succ u1) (succ u2)} (Prod.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} (Set.hasCoeToSort.{u1} B) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) F) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (Homeomorph.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} Z) Type.{u3} 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 Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_applyₓ'. -/
 @[simp]
 theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
@@ -859,7 +859,7 @@ theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
 lean 3 declaration is
   forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (p : Prod.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} (Set.hasCoeToSort.{u1} B) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) F), Eq.{succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} Z) Type.{u3} (Set.hasCoeToSort.{u3} Z) (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (Homeomorph.{max u1 u2, u3} (Prod.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod_symm_apply Trivialization.sourceHomeomorphBaseSetProd_symm_applyₓ'. -/
 @[simp]
 theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
@@ -885,7 +885,7 @@ def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b}
 lean 3 declaration is
   forall {B : Type.{u_2}} {F : Type.{u_3}} {Z : Type.{u_5}} [_inst_1 : TopologicalSpace.{u_2} B] [_inst_2 : TopologicalSpace.{u_3} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u_5} Z] (e : Trivialization.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (hb : Membership.Mem.{u_2, u_2} B (Set.{u_2} B) (Set.hasMem.{u_2} B) b (Trivialization.baseSet.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))), Eq.{succ u_3} F (coeFn.{max (succ u_5) (succ u_3), max (succ u_5) (succ u_3)} (Homeomorph.{u_5, u_3} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) F (Subtype.topologicalSpace.{u_5} Z (fun (x : Z) => Membership.Mem.{u_5, u_5} Z (Set.{u_5} Z) (Set.hasMem.{u_5} Z) x (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) _inst_3) _inst_2) (fun (_x : Homeomorph.{u_5, u_3} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) F (Subtype.topologicalSpace.{u_5} Z (fun (x : Z) => Membership.Mem.{u_5, u_5} Z (Set.{u_5} Z) (Set.hasMem.{u_5} Z) x (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) _inst_3) _inst_2) => (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) -> F) (Homeomorph.hasCoeToFun.{u_5, u_3} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) F (Subtype.topologicalSpace.{u_5} Z (fun (x : Z) => Membership.Mem.{u_5, u_5} Z (Set.{u_5} Z) (Set.hasMem.{u_5} Z) x (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) _inst_3) _inst_2) (Trivialization.preimageSingletonHomeomorph.{u_2, u_3, u_5, u_1} B F Z _inst_1 _inst_2 proj _inst_3 e b hb) p) (Prod.snd.{u_2, u_3} B F (coeFn.{max (succ u_2) (succ u_3) (succ u_5), max (succ u_5) (succ u_2) (succ u_3)} (Trivialization.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 _inst_3 proj) (fun (_x : Trivialization.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 _inst_3 proj) => Z -> (Prod.{u_2, u_3} B F)) (Trivialization.hasCoeToFun.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 proj _inst_3) e ((fun (a : Type.{u_5}) (b : Type.{u_5}) [self : HasLiftT.{succ u_5, succ u_5} a b] => self.0) (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) Z (HasLiftT.mk.{succ u_5, succ u_5} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) Z (CoeTCₓ.coe.{succ u_5, succ u_5} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) Z (coeBase.{succ u_5, succ u_5} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) Z (coeSubtype.{succ u_5} Z (fun (x : Z) => Membership.Mem.{u_5, u_5} Z (Set.{u_5} Z) (Set.hasMem.{u_5} Z) x (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))))))) p)))
 but is expected to have type
-  forall {B : Type.{u_1}} {F : Type.{u_2}} {Z : Type.{u_3}} [_inst_1 : TopologicalSpace.{u_1} B] [_inst_2 : TopologicalSpace.{u_2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u_3} Z] (e : Trivialization.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (hb : Membership.mem.{u_1, u_1} B (Set.{u_1} B) (Set.instMembershipSet.{u_1} B) b (Trivialization.baseSet.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))), Eq.{succ u_2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) => F) p) (FunLike.coe.{max (succ u_2) (succ u_3), succ u_3, succ u_2} (Homeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2) (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) (fun (_x : Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) => F) _x) (EmbeddingLike.toFunLike.{max (succ u_2) (succ u_3), succ u_3, succ u_2} (Homeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2) (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (EquivLike.toEmbeddingLike.{max (succ u_2) (succ u_3), succ u_3, succ u_2} (Homeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2) (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (Homeomorph.instEquivLikeHomeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2))) (Trivialization.preimageSingletonHomeomorph.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 proj _inst_3 e b hb) p) (Prod.snd.{u_1, u_2} B F (Trivialization.toFun'.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 proj _inst_3 e (Subtype.val.{succ u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) p)))
+  forall {B : Type.{u_1}} {F : Type.{u_2}} {Z : Type.{u_3}} [_inst_1 : TopologicalSpace.{u_1} B] [_inst_2 : TopologicalSpace.{u_2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u_3} Z] (e : Trivialization.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (hb : Membership.mem.{u_1, u_1} B (Set.{u_1} B) (Set.instMembershipSet.{u_1} B) b (Trivialization.baseSet.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))), Eq.{succ u_2} F (FunLike.coe.{max (succ u_3) (succ u_2), succ u_3, succ u_2} (Homeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2) (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) (fun (_x : Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) => F) (EmbeddingLike.toFunLike.{max (succ u_3) (succ u_2), succ u_3, succ u_2} (Homeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2) (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (EquivLike.toEmbeddingLike.{max (succ u_3) (succ u_2), succ u_3, succ u_2} (Homeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2) (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (Homeomorph.instEquivLikeHomeomorph.{u_3, u_2} (Set.Elem.{u_3} Z (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) F (instTopologicalSpaceSubtype.{u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) _inst_3) _inst_2))) (Trivialization.preimageSingletonHomeomorph.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 proj _inst_3 e b hb) p) (Prod.snd.{u_1, u_2} B F (Trivialization.toFun'.{u_1, u_2, u_3} B F Z _inst_1 _inst_2 proj _inst_3 e (Subtype.val.{succ u_3} Z (fun (x : Z) => Membership.mem.{u_3, u_3} Z (Set.{u_3} Z) (Set.instMembershipSet.{u_3} Z) x (Set.preimage.{u_3, u_1} Z B proj (Singleton.singleton.{u_1, u_1} B (Set.{u_1} B) (Set.instSingletonSet.{u_1} B) b))) p)))
 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_applyₓ'. -/
 @[simp]
 theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : proj ⁻¹' {b}) :
@@ -897,7 +897,7 @@ theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : pr
 lean 3 declaration is
   forall {B : Type.{u_2}} {F : Type.{u_3}} {Z : Type.{u_5}} [_inst_1 : TopologicalSpace.{u_2} B] [_inst_2 : TopologicalSpace.{u_3} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u_5} Z] (e : Trivialization.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (hb : Membership.Mem.{u_2, u_2} B (Set.{u_2} B) (Set.hasMem.{u_2} B) b (Trivialization.baseSet.{u_2, u_3, u_5} B F Z _inst_1 _inst_2 _inst_3 proj e)) (p : F), Eq.{succ u_5} (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) (coeFn.{max (succ u_3) (succ u_5), max (succ u_3) (succ u_5)} (Homeomorph.{u_3, u_5} F (coeSort.{max (succ u_5) 1, succ (succ u_5)} (Set.{u_5} Z) Type.{u_5} (Set.hasCoeToSort.{u_5} Z) (Set.preimage.{u_5, u_2} Z B proj (Singleton.singleton.{u_2, u_2} B (Set.{u_2} B) (Set.hasSingleton.{u_2} B) b))) _inst_2 (Subtype.topologicalSpace.{u_5} Z (fun (x 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph_symm_apply Trivialization.preimageSingletonHomeomorph_symm_applyₓ'. -/
 @[simp]
 theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p : F) :
@@ -921,7 +921,7 @@ theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
 lean 3 declaration is
   forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z], (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) -> (forall {Z' : Type.{u4}} [_inst_5 : TopologicalSpace.{u4} Z'] (h : Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3), Trivialization.{u1, u2, u4} B F Z' _inst_1 _inst_2 _inst_5 (Function.comp.{succ u4, succ u3, succ u1} Z' Z B proj (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) (fun (_x : Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) => Z' -> Z) (Homeomorph.hasCoeToFun.{u4, u3} Z' Z _inst_5 _inst_3) h)))
 but is expected to have type
-  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z], (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) -> (forall {Z' : Type.{u4}} [_inst_5 : TopologicalSpace.{u4} Z'] (h : Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3), Trivialization.{u1, u2, u4} B F Z' _inst_1 _inst_2 _inst_5 (Function.comp.{succ u4, succ u3, succ u1} Z' Z B proj (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) Z' (fun (_x : Z') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Z') => Z) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u4), succ u4, succ u3} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) Z' Z (EquivLike.toEmbeddingLike.{max (succ u3) (succ u4), succ u4, succ u3} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) Z' Z (Homeomorph.instEquivLikeHomeomorph.{u4, u3} Z' Z _inst_5 _inst_3))) h)))
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z], (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) -> (forall {Z' : Type.{u4}} [_inst_5 : TopologicalSpace.{u4} Z'] (h : Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3), Trivialization.{u1, u2, u4} B F Z' _inst_1 _inst_2 _inst_5 (Function.comp.{succ u4, succ u3, succ u1} Z' Z B proj (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) Z' (fun (_x : Z') => Z) (EmbeddingLike.toFunLike.{max (succ u4) (succ u3), succ u4, succ u3} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) Z' Z (EquivLike.toEmbeddingLike.{max (succ u4) (succ u3), succ u4, succ u3} (Homeomorph.{u4, u3} Z' Z _inst_5 _inst_3) Z' Z (Homeomorph.instEquivLikeHomeomorph.{u4, u3} Z' Z _inst_5 _inst_3))) h)))
 Case conversion may be inaccurate. Consider using '#align trivialization.comp_homeomorph Trivialization.compHomeomorphₓ'. -/
 /-- Composition of a `trivialization` and a `homeomorph`. -/
 protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
@@ -1175,7 +1175,7 @@ def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization
 lean 3 declaration is
   forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] {F' : Type.{u4}} [_inst_5 : TopologicalSpace.{u4} F'] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (h : Homeomorph.{u2, u4} F F' _inst_2 _inst_5) (x : Z), Eq.{max (succ u1) (succ u4)} (Prod.{u1, u4} B F') (coeFn.{max (succ u1) (succ u4) (succ u3), max (succ u3) (succ u1) (succ u4)} (Trivialization.{u1, u4, u3} B F' Z _inst_1 _inst_5 _inst_3 proj) (fun (_x : Trivialization.{u1, u4, u3} B F' Z _inst_1 _inst_5 _inst_3 proj) => Z -> (Prod.{u1, u4} B F')) (Trivialization.hasCoeToFun.{u1, u4, u3} B F' Z _inst_1 _inst_5 proj _inst_3) (Trivialization.transFiberHomeomorph.{u1, u2, u3, u4} B F Z _inst_1 _inst_2 proj _inst_3 F' _inst_5 e h) x) (Prod.mk.{u1, u4} B F' (Prod.fst.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (fun (_x : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) => Z -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3) e x)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) (fun (_x : Homeomorph.{u2, u4} F F' _inst_2 _inst_5) => F -> F') (Homeomorph.hasCoeToFun.{u2, u4} F F' _inst_2 _inst_5) h (Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (fun (_x : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) => Z -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3) e x))))
 but is expected to have type
-  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] {F' : Type.{u4}} [_inst_5 : TopologicalSpace.{u4} F'] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (h : Homeomorph.{u2, u4} F F' _inst_2 _inst_5) (x : Z), Eq.{max (succ u3) (succ u4)} (Prod.{u3, u4} B F') (Trivialization.toFun'.{u3, u4, u1} B F' Z _inst_1 _inst_5 proj _inst_3 (Trivialization.transFiberHomeomorph.{u3, u2, u1, u4} B F Z _inst_1 _inst_2 proj _inst_3 F' _inst_5 e h) x) (Prod.mk.{u3, u4} B ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : F) => F') (Prod.snd.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e x))) (Prod.fst.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) F (fun (_x : F) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : F) => F') _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u4), succ u2, succ u4} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) F F' (EquivLike.toEmbeddingLike.{max (succ u2) (succ u4), succ u2, succ u4} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) F F' (Homeomorph.instEquivLikeHomeomorph.{u2, u4} F F' _inst_2 _inst_5))) h (Prod.snd.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e x))))
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] {F' : Type.{u4}} [_inst_5 : TopologicalSpace.{u4} F'] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (h : Homeomorph.{u2, u4} F F' _inst_2 _inst_5) (x : Z), Eq.{max (succ u3) (succ u4)} (Prod.{u3, u4} B F') (Trivialization.toFun'.{u3, u4, u1} B F' Z _inst_1 _inst_5 proj _inst_3 (Trivialization.transFiberHomeomorph.{u3, u2, u1, u4} B F Z _inst_1 _inst_2 proj _inst_3 F' _inst_5 e h) x) (Prod.mk.{u3, u4} B F' (Prod.fst.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) F (fun (_x : F) => F') (EmbeddingLike.toFunLike.{max (succ u2) (succ u4), succ u2, succ u4} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) F F' (EquivLike.toEmbeddingLike.{max (succ u2) (succ u4), succ u2, succ u4} (Homeomorph.{u2, u4} F F' _inst_2 _inst_5) F F' (Homeomorph.instEquivLikeHomeomorph.{u2, u4} F F' _inst_2 _inst_5))) h (Prod.snd.{u3, u2} B F (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e x))))
 Case conversion may be inaccurate. Consider using '#align trivialization.trans_fiber_homeomorph_apply Trivialization.transFiberHomeomorph_applyₓ'. -/
 @[simp]
 theorem transFiberHomeomorph_apply {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
@@ -1292,7 +1292,7 @@ protected def coordChangeHomeomorph (e₁ e₂ : Trivialization F proj) {b : B}
 lean 3 declaration is
   forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e₁ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (h₁ : Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) (h₂ : Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₂)), Eq.{succ u2} (F -> F) (coeFn.{succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) (fun (_x : Homeomorph.{u2, u2} F F _inst_2 _inst_2) => F -> F) (Homeomorph.hasCoeToFun.{u2, u2} F F _inst_2 _inst_2) (Trivialization.coordChangeHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b h₁ h₂)) (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b)
 but is expected to have type
-  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e₁ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (h₁ : Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) (h₂ : Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₂)), Eq.{succ u2} (forall (ᾰ : F), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : F) => F) ᾰ) (FunLike.coe.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F (fun (_x : F) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : F) => F) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F F (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F F (Homeomorph.instEquivLikeHomeomorph.{u2, u2} F F _inst_2 _inst_2))) (Trivialization.coordChangeHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b h₁ h₂)) (Trivialization.coordChange.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b)
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e₁ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (h₁ : Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) (h₂ : Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₂)), Eq.{succ u2} (F -> F) (FunLike.coe.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F (fun (_x : F) => F) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F F (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F F (Homeomorph.instEquivLikeHomeomorph.{u2, u2} F F _inst_2 _inst_2))) (Trivialization.coordChangeHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b h₁ h₂)) (Trivialization.coordChange.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b)
 Case conversion may be inaccurate. Consider using '#align trivialization.coord_change_homeomorph_coe Trivialization.coordChangeHomeomorph_coeₓ'. -/
 @[simp]
 theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)

bump to nightly-2023-03-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.LocalHomeomorph
 /-!
 # Trivializations
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 ### Basic definitions

bump to nightly-2023-03-10-08

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

f582169b

Diff

@@ -61,6 +61,7 @@ variable {ι : Type _} {B : Type _} {F : Type _} {E : B → Type _}
 
 variable (F) {Z : Type _} [TopologicalSpace B] [TopologicalSpace F] {proj : Z → B}
 
+#print Pretrivialization /-
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- This structure contains the information left for a local trivialization (which is implemented
 below as `trivialization F proj`) if the total space has not been given a topology, but we
@@ -76,6 +77,7 @@ structure Pretrivialization (proj : Z → B) extends LocalEquiv Z (B × F) where
   target_eq : target = base_set ×ˢ univ
   proj_toFun : ∀ p ∈ source, (to_fun p).1 = proj p
 #align pretrivialization Pretrivialization
+-/
 
 namespace Pretrivialization
 
@@ -84,79 +86,177 @@ instance : CoeFun (Pretrivialization F proj) fun _ => Z → B × F :=
 
 variable {F} (e : Pretrivialization F proj) {x : Z}
 
+/- warning: pretrivialization.coe_coe -> Pretrivialization.coe_coe is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj), Eq.{max (succ u3) (succ (max u1 u2))} (Z -> (Prod.{u1, u2} B F)) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F)) (fun (_x : LocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F)) => Z -> (Prod.{u1, u2} B F)) (LocalEquiv.hasCoeToFun.{u3, max u1 u2} Z (Prod.{u1, u2} B F)) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (fun (_x : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) => Z -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) e)
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 proj), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Z -> (Prod.{u3, u2} B F)) (LocalEquiv.toFun.{u1, max u3 u2} Z (Prod.{u3, u2} B F) (Pretrivialization.toLocalEquiv.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e)
+Case conversion may be inaccurate. Consider using '#align pretrivialization.coe_coe Pretrivialization.coe_coeₓ'. -/
 @[simp, mfld_simps]
 theorem coe_coe : ⇑e.toLocalEquiv = e :=
   rfl
 #align pretrivialization.coe_coe Pretrivialization.coe_coe
 
+/- warning: pretrivialization.coe_fst -> Pretrivialization.coe_fst is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) {x : Z}, (Membership.Mem.{u3, u3} Z (Set.{u3} Z) (Set.hasMem.{u3} Z) x (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e))) -> (Eq.{succ u1} B (Prod.fst.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (fun (_x : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) => Z -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) e x)) (proj x))
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] {proj : Z -> B} (e : Pretrivialization.{u2, u1, u3} B F Z _inst_1 _inst_2 proj) {x : Z}, (Membership.mem.{u3, u3} Z (Set.{u3} Z) (Set.instMembershipSet.{u3} Z) x (LocalEquiv.source.{u3, max u2 u1} Z (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, u3} B F Z _inst_1 _inst_2 proj e))) -> (Eq.{succ u2} B (Prod.fst.{u2, u1} B F (Pretrivialization.toFun'.{u2, u1, u3} B F Z _inst_1 _inst_2 proj e x)) (proj x))
+Case conversion may be inaccurate. Consider using '#align pretrivialization.coe_fst Pretrivialization.coe_fstₓ'. -/
 @[simp, mfld_simps]
 theorem coe_fst (ex : x ∈ e.source) : (e x).1 = proj x :=
   e.proj_toFun x ex
 #align pretrivialization.coe_fst Pretrivialization.coe_fst
 
+/- warning: pretrivialization.mem_source -> Pretrivialization.mem_source is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) {x : Z}, Iff (Membership.Mem.{u3, u3} Z (Set.{u3} Z) (Set.hasMem.{u3} Z) x (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e))) (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) (proj x) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e))
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] {proj : Z -> B} (e : Pretrivialization.{u2, u1, u3} B F Z _inst_1 _inst_2 proj) {x : Z}, Iff (Membership.mem.{u3, u3} Z (Set.{u3} Z) (Set.instMembershipSet.{u3} Z) x (LocalEquiv.source.{u3, max u2 u1} Z (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, u3} B F Z _inst_1 _inst_2 proj e))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (proj x) (Pretrivialization.baseSet.{u2, u1, u3} B F Z _inst_1 _inst_2 proj e))
+Case conversion may be inaccurate. Consider using '#align pretrivialization.mem_source Pretrivialization.mem_sourceₓ'. -/
 theorem mem_source : x ∈ e.source ↔ proj x ∈ e.baseSet := by rw [e.source_eq, mem_preimage]
 #align pretrivialization.mem_source Pretrivialization.mem_source
 
+/- warning: pretrivialization.coe_fst' -> Pretrivialization.coe_fst' is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) {x : Z}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) (proj x) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) -> (Eq.{succ u1} B (Prod.fst.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (fun (_x : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) => Z -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) e x)) (proj x))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 proj) {x : Z}, (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (proj x) (Pretrivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e)) -> (Eq.{succ u3} B (Prod.fst.{u3, u2} B F (Pretrivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e x)) (proj x))
+Case conversion may be inaccurate. Consider using '#align pretrivialization.coe_fst' Pretrivialization.coe_fst'ₓ'. -/
 theorem coe_fst' (ex : proj x ∈ e.baseSet) : (e x).1 = proj x :=
   e.coe_fst (e.mem_source.2 ex)
 #align pretrivialization.coe_fst' Pretrivialization.coe_fst'
 
+/- warning: pretrivialization.eq_on -> Pretrivialization.eqOn is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.eq_on Pretrivialization.eqOnₓ'. -/
 protected theorem eqOn : EqOn (Prod.fst ∘ e) proj e.source := fun x hx => e.coe_fst hx
 #align pretrivialization.eq_on Pretrivialization.eqOn
 
+/- warning: pretrivialization.mk_proj_snd -> Pretrivialization.mk_proj_snd is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.mk_proj_snd Pretrivialization.mk_proj_sndₓ'. -/
 theorem mk_proj_snd (ex : x ∈ e.source) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst ex).symm rfl
 #align pretrivialization.mk_proj_snd Pretrivialization.mk_proj_snd
 
+/- warning: pretrivialization.mk_proj_snd' -> Pretrivialization.mk_proj_snd' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.mk_proj_snd' Pretrivialization.mk_proj_snd'ₓ'. -/
 theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst' ex).symm rfl
 #align pretrivialization.mk_proj_snd' Pretrivialization.mk_proj_snd'
 
+#print Pretrivialization.setSymm /-
 /-- Composition of inverse and coercion from the subtype of the target. -/
 def setSymm : e.target → Z :=
   e.target.restrict e.toLocalEquiv.symm
 #align pretrivialization.set_symm Pretrivialization.setSymm
+-/
 
+/- warning: pretrivialization.mem_target -> Pretrivialization.mem_target is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.mem_target Pretrivialization.mem_targetₓ'. -/
 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
   rw [e.target_eq, prod_univ, mem_preimage]
 #align pretrivialization.mem_target Pretrivialization.mem_target
 
+/- warning: pretrivialization.proj_symm_apply -> Pretrivialization.proj_symm_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_applyₓ'. -/
 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEquiv.symm x) = x.1 :=
   by
   have := (e.coe_fst (e.to_local_equiv.map_target hx)).symm
   rwa [← e.coe_coe, e.to_local_equiv.right_inv hx] at this
 #align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_apply
 
+/- warning: pretrivialization.proj_symm_apply' -> Pretrivialization.proj_symm_apply' is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) {b : B} {x : F}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) -> (Eq.{succ u1} B (proj (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LocalEquiv.{max u1 u2, u3} (Prod.{u1, u2} B F) Z) (fun (_x : LocalEquiv.{max u1 u2, u3} (Prod.{u1, u2} B F) Z) => (Prod.{u1, u2} B F) -> Z) (LocalEquiv.hasCoeToFun.{max u1 u2, u3} (Prod.{u1, u2} B F) Z) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (Prod.mk.{u1, u2} B F b x))) b)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.proj_symm_apply' Pretrivialization.proj_symm_apply'ₓ'. -/
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     proj (e.toLocalEquiv.symm (b, x)) = b :=
   e.proj_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.proj_symm_apply' Pretrivialization.proj_symm_apply'
 
+/- warning: pretrivialization.proj_surj_on_base_set -> Pretrivialization.proj_surjOn_baseSet is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) [_inst_3 : Nonempty.{succ u2} F], Set.SurjOn.{u3, u1} Z B proj (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)
+but is expected to have type
+  forall {B : Type.{u1}} {F : Type.{u3}} {Z : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u3} F] {proj : Z -> B} (e : Pretrivialization.{u1, u3, u2} B F Z _inst_1 _inst_2 proj) [_inst_3 : Nonempty.{succ u3} F], Set.SurjOn.{u2, u1} Z B proj (LocalEquiv.source.{u2, max u1 u3} Z (Prod.{u1, u3} B F) (Pretrivialization.toLocalEquiv.{u1, u3, u2} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.baseSet.{u1, u3, u2} B F Z _inst_1 _inst_2 proj e)
+Case conversion may be inaccurate. Consider using '#align pretrivialization.proj_surj_on_base_set Pretrivialization.proj_surjOn_baseSetₓ'. -/
 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet := fun b hb =>
   let ⟨y⟩ := ‹Nonempty F›
   ⟨e.toLocalEquiv.symm (b, y), e.toLocalEquiv.map_target <| e.mem_target.2 hb,
     e.proj_symm_apply' hb⟩
 #align pretrivialization.proj_surj_on_base_set Pretrivialization.proj_surjOn_baseSet
 
+/- warning: pretrivialization.apply_symm_apply -> Pretrivialization.apply_symm_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.apply_symm_apply Pretrivialization.apply_symm_applyₓ'. -/
 theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalEquiv.symm x) = x :=
   e.toLocalEquiv.right_inv hx
 #align pretrivialization.apply_symm_apply Pretrivialization.apply_symm_apply
 
+/- warning: pretrivialization.apply_symm_apply' -> Pretrivialization.apply_symm_apply' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.apply_symm_apply' Pretrivialization.apply_symm_apply'ₓ'. -/
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     e (e.toLocalEquiv.symm (b, x)) = (b, x) :=
   e.apply_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.apply_symm_apply' Pretrivialization.apply_symm_apply'
 
+/- warning: pretrivialization.symm_apply_apply -> Pretrivialization.symm_apply_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) {x : Z}, (Membership.Mem.{u3, u3} Z (Set.{u3} Z) (Set.hasMem.{u3} Z) x (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e))) -> (Eq.{succ u3} Z (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LocalEquiv.{max u1 u2, u3} (Prod.{u1, u2} B F) Z) (fun (_x : LocalEquiv.{max u1 u2, u3} (Prod.{u1, u2} B F) Z) => (Prod.{u1, u2} B F) -> Z) (LocalEquiv.hasCoeToFun.{max u1 u2, u3} (Prod.{u1, u2} B F) Z) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (fun (_x : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) => Z -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) e x)) x)
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_apply_apply Pretrivialization.symm_apply_applyₓ'. -/
 theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toLocalEquiv.symm (e x) = x :=
   e.toLocalEquiv.left_inv hx
 #align pretrivialization.symm_apply_apply Pretrivialization.symm_apply_apply
 
+/- warning: pretrivialization.symm_apply_mk_proj -> Pretrivialization.symm_apply_mk_proj is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_projₓ'. -/
 @[simp, mfld_simps]
 theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
     e.toLocalEquiv.symm (proj x, (e x).2) = x := by
   rw [← e.coe_fst ex, Prod.mk.eta, ← e.coe_coe, e.to_local_equiv.left_inv ex]
 #align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_proj
 
+/- warning: pretrivialization.preimage_symm_proj_base_set -> Pretrivialization.preimage_symm_proj_baseSet is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSetₓ'. -/
 @[simp, mfld_simps]
 theorem preimage_symm_proj_baseSet :
     e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target :=
@@ -166,6 +266,12 @@ theorem preimage_symm_proj_baseSet :
   exact e.mem_target.mp hx
 #align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSet
 
+/- warning: pretrivialization.preimage_symm_proj_inter -> Pretrivialization.preimage_symm_proj_inter is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.preimage_symm_proj_inter Pretrivialization.preimage_symm_proj_interₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, mfld_simps]
@@ -179,23 +285,47 @@ theorem preimage_symm_proj_inter (s : Set B) :
   rw [e.proj_symm_apply' h]
 #align pretrivialization.preimage_symm_proj_inter Pretrivialization.preimage_symm_proj_inter
 
+/- warning: pretrivialization.target_inter_preimage_symm_source_eq -> Pretrivialization.target_inter_preimage_symm_source_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.target_inter_preimage_symm_source_eq Pretrivialization.target_inter_preimage_symm_source_eqₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem target_inter_preimage_symm_source_eq (e f : Pretrivialization F proj) :
     f.target ∩ f.toLocalEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [inter_comm, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]
 #align pretrivialization.target_inter_preimage_symm_source_eq Pretrivialization.target_inter_preimage_symm_source_eq
 
+/- warning: pretrivialization.trans_source -> Pretrivialization.trans_source is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (f : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (LocalEquiv.source.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Prod.{u1, u2} B F) (LocalEquiv.trans.{max u1 u2, u3, max u1 u2} (Prod.{u1, u2} B F) Z (Prod.{u1, u2} B F) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj f)) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e))) (Set.prod.{u1, u2} B F (Inter.inter.{u1} (Set.{u1} B) (Set.hasInter.{u1} B) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj f)) (Set.univ.{u2} F))
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.trans_source Pretrivialization.trans_sourceₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem trans_source (e f : Pretrivialization F proj) :
     (f.toLocalEquiv.symm.trans e.toLocalEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [LocalEquiv.trans_source, LocalEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
 #align pretrivialization.trans_source Pretrivialization.trans_source
 
+/- warning: pretrivialization.symm_trans_symm -> Pretrivialization.symm_trans_symm is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (e' : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj), Eq.{succ (max u1 u2)} (LocalEquiv.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Prod.{u1, u2} B F)) (LocalEquiv.symm.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Prod.{u1, u2} B F) (LocalEquiv.trans.{max u1 u2, u3, max u1 u2} (Prod.{u1, u2} B F) Z (Prod.{u1, u2} B F) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e'))) (LocalEquiv.trans.{max u1 u2, u3, max u1 u2} (Prod.{u1, u2} B F) Z (Prod.{u1, u2} B F) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e')) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symmₓ'. -/
 theorem symm_trans_symm (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm = e'.toLocalEquiv.symm.trans e.toLocalEquiv :=
   by rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
 #align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symm
 
+/- warning: pretrivialization.symm_trans_source_eq -> Pretrivialization.symm_trans_source_eq is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (e' : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (LocalEquiv.source.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Prod.{u1, u2} B F) (LocalEquiv.trans.{max u1 u2, u3, max u1 u2} (Prod.{u1, u2} B F) Z (Prod.{u1, u2} B F) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e'))) (Set.prod.{u1, u2} B F (Inter.inter.{u1} (Set.{u1} B) (Set.hasInter.{u1} B) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e')) (Set.univ.{u2} F))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_trans_source_eq Pretrivialization.symm_trans_source_eqₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
@@ -203,6 +333,12 @@ theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
     e.preimage_symm_proj_inter, inter_comm]
 #align pretrivialization.symm_trans_source_eq Pretrivialization.symm_trans_source_eq
 
+/- warning: pretrivialization.symm_trans_target_eq -> Pretrivialization.symm_trans_target_eq is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj) (e' : Pretrivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 proj), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (LocalEquiv.target.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Prod.{u1, u2} B F) (LocalEquiv.trans.{max u1 u2, u3, max u1 u2} (Prod.{u1, u2} B F) Z (Prod.{u1, u2} B F) (LocalEquiv.symm.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.toLocalEquiv.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e'))) (Set.prod.{u1, u2} B F (Inter.inter.{u1} (Set.{u1} B) (Set.hasInter.{u1} B) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e) (Pretrivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 proj e')) (Set.univ.{u2} F))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} (e : Pretrivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 proj) (e' : Pretrivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 proj), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (LocalEquiv.target.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (LocalEquiv.trans.{max u3 u2, u1, max u3 u2} (Prod.{u3, u2} B F) Z (Prod.{u3, u2} B F) (LocalEquiv.symm.{u1, max u3 u2} Z (Prod.{u3, u2} B F) (Pretrivialization.toLocalEquiv.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e)) (Pretrivialization.toLocalEquiv.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e'))) (Set.prod.{u3, u2} B F (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (Pretrivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e) (Pretrivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 proj e')) (Set.univ.{u2} F))
+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_trans_target_eq Pretrivialization.symm_trans_target_eqₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
@@ -211,19 +347,43 @@ theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
 
 variable {B F} (e' : Pretrivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
 
+/- warning: pretrivialization.coe_mem_source -> Pretrivialization.coe_mem_source is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.coe_mem_source Pretrivialization.coe_mem_sourceₓ'. -/
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align pretrivialization.coe_mem_source Pretrivialization.coe_mem_source
 
+/- warning: pretrivialization.coe_coe_fst -> Pretrivialization.coe_coe_fst is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (e' : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B} {y : E b}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e')) -> (Eq.{succ u1} B (Prod.fst.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) e' ((fun (a : Type.{u3}) (b : Sort.{max (succ u1) (succ u3)}) [self : HasLiftT.{succ u3, max (succ u1) (succ u3)} a b] => self.0) (E b) (Bundle.TotalSpace.{u1, u3} B E) (HasLiftT.mk.{succ u3, max (succ u1) (succ u3)} (E b) (Bundle.TotalSpace.{u1, u3} B E) (CoeTCₓ.coe.{succ u3, max (succ u1) (succ u3)} (E b) (Bundle.TotalSpace.{u1, u3} B E) (Bundle.TotalSpace.hasCoeT.{u1, u3} B E b))) y))) b)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.coe_coe_fst Pretrivialization.coe_coe_fstₓ'. -/
 @[simp, mfld_simps]
 theorem coe_coe_fst (hb : b ∈ e'.baseSet) : (e' y).1 = b :=
   e'.coe_fst (e'.mem_source.2 hb)
 #align pretrivialization.coe_coe_fst Pretrivialization.coe_coe_fst
 
+/- warning: pretrivialization.mk_mem_target -> Pretrivialization.mk_mem_target is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (e' : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {x : B} {y : F}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Set.{max u1 u2} (Prod.{u1, u2} B F)) (Set.hasMem.{max u1 u2} (Prod.{u1, u2} B F)) (Prod.mk.{u1, u2} B F x y) (LocalEquiv.target.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e'))) (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) x (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e'))
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u3}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (e' : Pretrivialization.{u2, u3, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)) {x : B} {y : F}, Iff (Membership.mem.{max u3 u2, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.instMembershipSet.{max u2 u3} (Prod.{u2, u3} B F)) (Prod.mk.{u2, u3} B F x y) (LocalEquiv.target.{max u2 u1, max u2 u3} (Bundle.TotalSpace.{u2, u1} B E) (Prod.{u2, u3} B F) (Pretrivialization.toLocalEquiv.{u2, u3, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E) e'))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) x (Pretrivialization.baseSet.{u2, u3, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E) e'))
+Case conversion may be inaccurate. Consider using '#align pretrivialization.mk_mem_target Pretrivialization.mk_mem_targetₓ'. -/
 theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSet :=
   e'.mem_target
 #align pretrivialization.mk_mem_target Pretrivialization.mk_mem_target
 
+/- warning: pretrivialization.symm_coe_proj -> Pretrivialization.symm_coe_proj is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {x : B} {y : F} (e' : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) x (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e')) -> (Eq.{succ u1} B (Sigma.fst.{u1, u3} B (fun (x : B) => E x) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (fun (_x : LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e')) (Prod.mk.{u1, u2} B F x y))) x)
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {x : B} {y : F} (e' : Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E)), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x (Pretrivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E) e')) -> (Eq.{succ u3} B (Sigma.fst.{u3, u1} B (fun (x : B) => E x) (LocalEquiv.toFun.{max u3 u2, max u3 u1} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (LocalEquiv.symm.{max u3 u1, max u3 u2} (Bundle.TotalSpace.{u3, u1} B E) (Prod.{u3, u2} B F) (Pretrivialization.toLocalEquiv.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E) e')) (Prod.mk.{u3, u2} B F x y))) x)
+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_coe_proj Pretrivialization.symm_coe_projₓ'. -/
 theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π E)) (h : x ∈ e'.baseSet) :
     (e'.toLocalEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
@@ -233,6 +393,7 @@ section Zero
 
 variable [∀ x, Zero (E x)]
 
+#print Pretrivialization.symm /-
 /-- A fiberwise inverse to `e`. This is the function `F → E b` that induces a local inverse
 `B × F → total_space E` of `e` on `e.base_set`. It is defined to be `0` outside `e.base_set`. -/
 protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F) : E b :=
@@ -240,37 +401,80 @@ protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F
     cast (congr_arg E (e.proj_symm_apply' hb)) (e.toLocalEquiv.symm (b, y)).2
   else 0
 #align pretrivialization.symm Pretrivialization.symm
+-/
 
+/- warning: pretrivialization.symm_apply -> Pretrivialization.symm_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B} (hb : Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (y : F), Eq.{succ u3} (E b) (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e b y) (cast.{succ u3} (E (Sigma.fst.{u1, u3} B (fun (x : B) => E x) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (fun (_x : LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (Prod.mk.{u1, u2} B F b y)))) (E b) (congr_arg.{succ u1, succ (succ u3)} B Type.{u3} (Sigma.fst.{u1, u3} B (fun (x : B) => E x) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (fun (_x : LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (Prod.mk.{u1, u2} B F b y))) b E (Pretrivialization.symm_coe_proj.{u1, u2, u3} B F E _inst_1 _inst_2 b y e hb)) (Sigma.snd.{u1, u3} B (fun (x : B) => E x) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (fun (_x : LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (Prod.mk.{u1, u2} B F b y))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_apply Pretrivialization.symm_applyₓ'. -/
 theorem symm_apply (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
 
+/- warning: pretrivialization.symm_apply_of_not_mem -> Pretrivialization.symm_apply_of_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Not (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e))) -> (forall (y : F), Eq.{succ u3} (E b) (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e b y) (OfNat.ofNat.{u3} (E b) 0 (OfNat.mk.{u3} (E b) 0 (Zero.zero.{u3} (E b) (_inst_3 b)))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_apply_of_not_mem Pretrivialization.symm_apply_of_not_memₓ'. -/
 theorem symm_apply_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align pretrivialization.symm_apply_of_not_mem Pretrivialization.symm_apply_of_not_mem
 
+/- warning: pretrivialization.coe_symm_of_not_mem -> Pretrivialization.coe_symm_of_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Not (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e))) -> (Eq.{max (succ u2) (succ u3)} (F -> (E b)) (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e b) (OfNat.ofNat.{max u2 u3} (F -> (E b)) 0 (OfNat.mk.{max u2 u3} (F -> (E b)) 0 (Zero.zero.{max u2 u3} (F -> (E b)) (Pi.instZero.{u2, u3} F (fun (y : F) => E b) (fun (i : F) => _inst_3 b))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_memₓ'. -/
 theorem coe_symm_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) :
     (e.symm b : F → E b) = 0 :=
   funext fun y => dif_neg hb
 #align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_mem
 
+/- warning: pretrivialization.mk_symm -> Pretrivialization.mk_symm is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (forall (y : F), Eq.{max (succ u1) (succ u3)} (Bundle.TotalSpace.{u1, u3} B E) (Bundle.totalSpaceMk.{u1, u3} B E b (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e b y)) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (fun (_x : LocalEquiv.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E)) (LocalEquiv.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (Pretrivialization.toLocalEquiv.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (Prod.mk.{u1, u2} B F b y)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.mk_symm Pretrivialization.mk_symmₓ'. -/
 theorem mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     totalSpaceMk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
   rw [e.symm_apply hb, total_space.mk_cast, total_space.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
 
+/- warning: pretrivialization.symm_proj_apply -> Pretrivialization.symm_proj_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) (z : Bundle.TotalSpace.{u1, u3} B E), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) (Bundle.TotalSpace.proj.{u1, u3} B E z) (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (Eq.{succ u3} (E (Bundle.TotalSpace.proj.{u1, u3} B E z)) (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e (Bundle.TotalSpace.proj.{u1, u3} B E z) (Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) e z))) (Sigma.snd.{u1, u3} B (fun (x : B) => E x) z))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u1} (E x)] (e : Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E)) (z : Bundle.TotalSpace.{u3, u1} B E), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Bundle.TotalSpace.proj.{u3, u1} B E z) (Pretrivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E) e)) -> (Eq.{succ u1} (E (Bundle.TotalSpace.proj.{u3, u1} B E z)) (Pretrivialization.symm.{u3, u2, u1} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e (Bundle.TotalSpace.proj.{u3, u1} B E z) (Prod.snd.{u3, u2} B F (Pretrivialization.toFun'.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E) e z))) (Sigma.snd.{u3, u1} B (fun (x : B) => E x) z))
+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_proj_apply Pretrivialization.symm_proj_applyₓ'. -/
 theorem symm_proj_apply (e : Pretrivialization F (π E)) (z : TotalSpace E)
     (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 := by
   rw [e.symm_apply hz, cast_eq_iff_heq, e.mk_proj_snd' hz, e.symm_apply_apply (e.mem_source.mpr hz)]
 #align pretrivialization.symm_proj_apply Pretrivialization.symm_proj_apply
 
+/- warning: pretrivialization.symm_apply_apply_mk -> Pretrivialization.symm_apply_apply_mk is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (forall (y : E b), Eq.{succ u3} (E b) (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e b (Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) e (Bundle.totalSpaceMk.{u1, u3} B E b y)))) y)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.symm_apply_apply_mk Pretrivialization.symm_apply_apply_mkₓ'. -/
 theorem symm_apply_apply_mk (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
     e.symm b (e (totalSpaceMk b y)).2 = y :=
   e.symm_proj_apply (totalSpaceMk b y) hb
 #align pretrivialization.symm_apply_apply_mk Pretrivialization.symm_apply_apply_mk
 
+/- warning: pretrivialization.apply_mk_symm -> Pretrivialization.apply_mk_symm is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_3 : forall (x : B), Zero.{u3} (E x)] (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (forall (y : F), Eq.{max (succ u1) (succ u2)} (Prod.{u1, u2} B F) (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Pretrivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)) e (Bundle.totalSpaceMk.{u1, u3} B E b (Pretrivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 (fun (x : B) => _inst_3 x) e b y))) (Prod.mk.{u1, u2} B F b y))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pretrivialization.apply_mk_symm Pretrivialization.apply_mk_symmₓ'. -/
 theorem apply_mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e (totalSpaceMk b (e.symm b y)) = (b, y) := by
   rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
@@ -282,6 +486,7 @@ end Pretrivialization
 
 variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace E)]
 
+#print Trivialization /-
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A structure extending local homeomorphisms, defining a local trivialization of a projection
 `proj : Z → B` with fiber `F`, as a local homeomorphism between `Z` and `B × F` defined between two
@@ -295,15 +500,18 @@ structure Trivialization (proj : Z → B) extends LocalHomeomorph Z (B × F) whe
   target_eq : target = base_set ×ˢ univ
   proj_toFun : ∀ p ∈ source, (to_local_homeomorph p).1 = proj p
 #align trivialization Trivialization
+-/
 
 namespace Trivialization
 
 variable {F} (e : Trivialization F proj) {x : Z}
 
+#print Trivialization.toPretrivialization /-
 /-- Natural identification as a `pretrivialization`. -/
 def toPretrivialization : Pretrivialization F proj :=
   { e with }
 #align trivialization.to_pretrivialization Trivialization.toPretrivialization
+-/
 
 instance : CoeFun (Trivialization F proj) fun _ => Z → B × F :=
   ⟨fun e => e.toFun⟩
@@ -311,6 +519,12 @@ instance : CoeFun (Trivialization F proj) fun _ => Z → B × F :=
 instance : Coe (Trivialization F proj) (Pretrivialization F proj) :=
   ⟨toPretrivialization⟩
 
+/- warning: trivialization.to_pretrivialization_injective -> Trivialization.toPretrivialization_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.to_pretrivialization_injective Trivialization.toPretrivialization_injectiveₓ'. -/
 theorem toPretrivialization_injective :
     Function.Injective fun e : Trivialization F proj => e.toPretrivialization :=
   by
@@ -320,109 +534,253 @@ theorem toPretrivialization_injective :
   exact id
 #align trivialization.to_pretrivialization_injective Trivialization.toPretrivialization_injective
 
+/- warning: trivialization.coe_coe -> Trivialization.coe_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.coe_coe Trivialization.coe_coeₓ'. -/
 @[simp, mfld_simps]
 theorem coe_coe : ⇑e.toLocalHomeomorph = e :=
   rfl
 #align trivialization.coe_coe Trivialization.coe_coe
 
+/- warning: trivialization.coe_fst -> Trivialization.coe_fst is a dubious translation:
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 @[simp, mfld_simps]
 theorem coe_fst (ex : x ∈ e.source) : (e x).1 = proj x :=
   e.proj_toFun x ex
 #align trivialization.coe_fst Trivialization.coe_fst
 
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 protected theorem eqOn : EqOn (Prod.fst ∘ e) proj e.source := fun x hx => e.coe_fst hx
 #align trivialization.eq_on Trivialization.eqOn
 
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 theorem mem_source : x ∈ e.source ↔ proj x ∈ e.baseSet := by rw [e.source_eq, mem_preimage]
 #align trivialization.mem_source Trivialization.mem_source
 
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 theorem coe_fst' (ex : proj x ∈ e.baseSet) : (e x).1 = proj x :=
   e.coe_fst (e.mem_source.2 ex)
 #align trivialization.coe_fst' Trivialization.coe_fst'
 
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 theorem mk_proj_snd (ex : x ∈ e.source) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst ex).symm rfl
 #align trivialization.mk_proj_snd Trivialization.mk_proj_snd
 
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 theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
   Prod.ext (e.coe_fst' ex).symm rfl
 #align trivialization.mk_proj_snd' Trivialization.mk_proj_snd'
 
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 theorem source_inter_preimage_target_inter (s : Set (B × F)) :
     e.source ∩ e ⁻¹' (e.target ∩ s) = e.source ∩ e ⁻¹' s :=
   e.toLocalHomeomorph.source_inter_preimage_target_inter s
 #align trivialization.source_inter_preimage_target_inter Trivialization.source_inter_preimage_target_inter
 
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+Case conversion may be inaccurate. Consider using '#align trivialization.coe_mk Trivialization.coe_mkₓ'. -/
 @[simp, mfld_simps]
 theorem coe_mk (e : LocalHomeomorph Z (B × F)) (i j k l m) (x : Z) :
     (Trivialization.mk e i j k l m : Trivialization F proj) x = e x :=
   rfl
 #align trivialization.coe_mk Trivialization.coe_mk
 
+/- warning: trivialization.mem_target -> Trivialization.mem_target is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.mem_target Trivialization.mem_targetₓ'. -/
 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet :=
   e.toPretrivialization.mem_target
 #align trivialization.mem_target Trivialization.mem_target
 
+/- warning: trivialization.map_target -> Trivialization.map_target is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.map_target Trivialization.map_targetₓ'. -/
 theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toLocalHomeomorph.symm x ∈ e.source :=
   e.toLocalHomeomorph.map_target hx
 #align trivialization.map_target Trivialization.map_target
 
+/- warning: trivialization.proj_symm_apply -> Trivialization.proj_symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.proj_symm_apply Trivialization.proj_symm_applyₓ'. -/
 theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalHomeomorph.symm x) = x.1 :=
   e.toPretrivialization.proj_symm_apply hx
 #align trivialization.proj_symm_apply Trivialization.proj_symm_apply
 
+/- warning: trivialization.proj_symm_apply' -> Trivialization.proj_symm_apply' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.proj_symm_apply' Trivialization.proj_symm_apply'ₓ'. -/
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     proj (e.toLocalHomeomorph.symm (b, x)) = b :=
   e.toPretrivialization.proj_symm_apply' hx
 #align trivialization.proj_symm_apply' Trivialization.proj_symm_apply'
 
+/- warning: trivialization.proj_surj_on_base_set -> Trivialization.proj_surjOn_baseSet is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) [_inst_5 : Nonempty.{succ u2} F], Set.SurjOn.{u3, u1} Z B proj (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e))) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)
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 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet :=
   e.toPretrivialization.proj_surjOn_baseSet
 #align trivialization.proj_surj_on_base_set Trivialization.proj_surjOn_baseSet
 
+/- warning: trivialization.apply_symm_apply -> Trivialization.apply_symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.apply_symm_apply Trivialization.apply_symm_applyₓ'. -/
 theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalHomeomorph.symm x) = x :=
   e.toLocalHomeomorph.right_inv hx
 #align trivialization.apply_symm_apply Trivialization.apply_symm_apply
 
+/- warning: trivialization.apply_symm_apply' -> Trivialization.apply_symm_apply' is a dubious translation:
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 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
     e (e.toLocalHomeomorph.symm (b, x)) = (b, x) :=
   e.toPretrivialization.apply_symm_apply' hx
 #align trivialization.apply_symm_apply' Trivialization.apply_symm_apply'
 
+/- warning: trivialization.symm_apply_mk_proj -> Trivialization.symm_apply_mk_proj is a dubious translation:
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 @[simp, mfld_simps]
 theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toLocalHomeomorph.symm (proj x, (e x).2) = x :=
   e.toPretrivialization.symm_apply_mk_proj ex
 #align trivialization.symm_apply_mk_proj Trivialization.symm_apply_mk_proj
 
+/- warning: trivialization.symm_trans_source_eq -> Trivialization.symm_trans_source_eq is a dubious translation:
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_source_eq (e e' : Trivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_source_eq e.toPretrivialization e'
 #align trivialization.symm_trans_source_eq Trivialization.symm_trans_source_eq
 
+/- warning: trivialization.symm_trans_target_eq -> Trivialization.symm_trans_target_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.symm_trans_target_eq Trivialization.symm_trans_target_eqₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem symm_trans_target_eq (e e' : Trivialization F proj) :
     (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_target_eq e.toPretrivialization e'
 #align trivialization.symm_trans_target_eq Trivialization.symm_trans_target_eq
 
+/- warning: trivialization.coe_fst_eventually_eq_proj -> Trivialization.coe_fst_eventuallyEq_proj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.coe_fst_eventually_eq_proj Trivialization.coe_fst_eventuallyEq_projₓ'. -/
 theorem coe_fst_eventuallyEq_proj (ex : x ∈ e.source) : Prod.fst ∘ e =ᶠ[𝓝 x] proj :=
   mem_nhds_iff.2 ⟨e.source, fun y hy => e.coe_fst hy, e.open_source, ex⟩
 #align trivialization.coe_fst_eventually_eq_proj Trivialization.coe_fst_eventuallyEq_proj
 
+/- warning: trivialization.coe_fst_eventually_eq_proj' -> Trivialization.coe_fst_eventuallyEq_proj' is a dubious translation:
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+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {x : Z}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) (proj x) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (Filter.EventuallyEq.{u3, u1} Z B (nhds.{u3} Z _inst_3 x) (Function.comp.{succ u3, max (succ u1) (succ u2), succ u1} Z (Prod.{u1, u2} B F) B (Prod.fst.{u1, u2} B F) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (fun (_x : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) => Z -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3) e)) proj)
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+Case conversion may be inaccurate. Consider using '#align trivialization.coe_fst_eventually_eq_proj' Trivialization.coe_fst_eventuallyEq_proj'ₓ'. -/
 theorem coe_fst_eventuallyEq_proj' (ex : proj x ∈ e.baseSet) : Prod.fst ∘ e =ᶠ[𝓝 x] proj :=
   e.coe_fst_eventuallyEq_proj (e.mem_source.2 ex)
 #align trivialization.coe_fst_eventually_eq_proj' Trivialization.coe_fst_eventuallyEq_proj'
 
+/- warning: trivialization.map_proj_nhds -> Trivialization.map_proj_nhds is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {x : Z}, (Membership.Mem.{u3, u3} Z (Set.{u3} Z) (Set.hasMem.{u3} Z) x (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)))) -> (Eq.{succ u1} (Filter.{u1} B) (Filter.map.{u3, u1} Z B proj (nhds.{u3} Z _inst_3 x)) (nhds.{u1} B _inst_1 (proj x)))
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u2, u1, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {x : Z}, (Membership.mem.{u3, u3} Z (Set.{u3} Z) (Set.instMembershipSet.{u3} Z) x (LocalEquiv.source.{u3, max u2 u1} Z (Prod.{u2, u1} B F) (LocalHomeomorph.toLocalEquiv.{u3, max u2 u1} Z (Prod.{u2, u1} B F) _inst_3 (instTopologicalSpaceProd.{u2, u1} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u1, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)))) -> (Eq.{succ u2} (Filter.{u2} B) (Filter.map.{u3, u2} Z B proj (nhds.{u3} Z _inst_3 x)) (nhds.{u2} B _inst_1 (proj x)))
+Case conversion may be inaccurate. Consider using '#align trivialization.map_proj_nhds Trivialization.map_proj_nhdsₓ'. -/
 theorem map_proj_nhds (ex : x ∈ e.source) : map proj (𝓝 x) = 𝓝 (proj x) := by
   rw [← e.coe_fst ex, ← map_congr (e.coe_fst_eventually_eq_proj ex), ← map_map, ← e.coe_coe,
     e.to_local_homeomorph.map_nhds_eq ex, map_fst_nhds]
 #align trivialization.map_proj_nhds Trivialization.map_proj_nhds
 
+/- warning: trivialization.preimage_subset_source -> Trivialization.preimage_subset_source is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u1} B}, (HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) s (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (HasSubset.Subset.{u3} (Set.{u3} Z) (Set.hasSubset.{u3} Z) (Set.preimage.{u3, u1} Z B proj s) (LocalEquiv.source.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e))))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u3} B}, (HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) s (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (HasSubset.Subset.{u1} (Set.{u1} Z) (Set.instHasSubsetSet.{u1} Z) (Set.preimage.{u1, u3} Z B proj s) (LocalEquiv.source.{u1, max u3 u2} Z (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{u1, max u3 u2} Z (Prod.{u3, u2} B F) _inst_3 (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e))))
+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_subset_source Trivialization.preimage_subset_sourceₓ'. -/
 theorem preimage_subset_source {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ⊆ e.source :=
   fun p hp => e.mem_source.mpr (hb hp)
 #align trivialization.preimage_subset_source Trivialization.preimage_subset_source
 
+/- warning: trivialization.image_preimage_eq_prod_univ -> Trivialization.image_preimage_eq_prod_univ is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u1} B}, (HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) s (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (Set.image.{u3, max u1 u2} Z (Prod.{u1, u2} B F) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u3) (succ u1) (succ u2)} (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (fun (_x : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) => Z -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3) e) (Set.preimage.{u3, u1} Z B proj s)) (Set.prod.{u1, u2} B F s (Set.univ.{u2} F)))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u3} B}, (HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) s (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.image.{u1, max u3 u2} Z (Prod.{u3, u2} B F) (Trivialization.toFun'.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e) (Set.preimage.{u1, u3} Z B proj s)) (Set.prod.{u3, u2} B F s (Set.univ.{u2} F)))
+Case conversion may be inaccurate. Consider using '#align trivialization.image_preimage_eq_prod_univ Trivialization.image_preimage_eq_prod_univₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     e '' (proj ⁻¹' s) = s ×ˢ univ :=
@@ -434,6 +792,12 @@ theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     ⟨e.invFun p, mem_preimage.mpr ((e.proj_symm_apply hp').symm ▸ hp.1), e.apply_symm_apply hp'⟩
 #align trivialization.image_preimage_eq_prod_univ Trivialization.image_preimage_eq_prod_univ
 
+/- warning: trivialization.preimage_homeomorph -> Trivialization.preimageHomeomorph is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u1} B}, (HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) s (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (Homeomorph.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} Z) Type.{u3} (Set.hasCoeToSort.{u3} Z) (Set.preimage.{u3, u1} Z B proj s)) (Prod.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} (Set.hasCoeToSort.{u1} B) s) F) (Subtype.topologicalSpace.{u3} Z (fun (x : Z) => Membership.Mem.{u3, u3} Z (Set.{u3} Z) (Set.hasMem.{u3} Z) x (Set.preimage.{u3, u1} Z B proj s)) _inst_3) (Prod.topologicalSpace.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} B) Type.{u1} (Set.hasCoeToSort.{u1} B) s) F (Subtype.topologicalSpace.{u1} B (fun (x : B) => Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) x s) _inst_1) _inst_2))
+but is expected to have type
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {s : Set.{u1} B}, (HasSubset.Subset.{u1} (Set.{u1} B) (Set.instHasSubsetSet.{u1} B) s (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (Homeomorph.{u3, max u2 u1} (Set.Elem.{u3} Z (Set.preimage.{u3, u1} Z B proj s)) (Prod.{u1, u2} (Set.Elem.{u1} B s) F) (instTopologicalSpaceSubtype.{u3} Z (fun (x : Z) => Membership.mem.{u3, u3} Z (Set.{u3} Z) (Set.instMembershipSet.{u3} Z) x (Set.preimage.{u3, u1} Z B proj s)) _inst_3) (instTopologicalSpaceProd.{u1, u2} (Set.Elem.{u1} B s) F (instTopologicalSpaceSubtype.{u1} B (fun (x : B) => Membership.mem.{u1, u1} B (Set.{u1} B) (Set.instMembershipSet.{u1} B) x s) _inst_1) _inst_2))
+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph Trivialization.preimageHomeomorphₓ'. -/
 /-- The preimage of a subset of the base set is homeomorphic to the product with the fiber. -/
 def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ s × F :=
   (e.toLocalHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
@@ -441,29 +805,59 @@ def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ
     ((Homeomorph.Set.prod s univ).trans ((Homeomorph.refl s).prodCongr (Homeomorph.Set.univ F)))
 #align trivialization.preimage_homeomorph Trivialization.preimageHomeomorph
 
+/- warning: trivialization.preimage_homeomorph_apply -> Trivialization.preimageHomeomorph_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_applyₓ'. -/
 @[simp]
 theorem preimageHomeomorph_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : proj ⁻¹' s) :
     e.preimageHomeomorph hb p = (⟨proj p, p.2⟩, (e p).2) :=
   Prod.ext (Subtype.ext (e.proj_toFun p (e.mem_source.mpr (hb p.2)))) rfl
 #align trivialization.preimage_homeomorph_apply Trivialization.preimageHomeomorph_apply
 
+/- warning: trivialization.preimage_homeomorph_symm_apply -> Trivialization.preimageHomeomorph_symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_homeomorph_symm_apply Trivialization.preimageHomeomorph_symm_applyₓ'. -/
 @[simp]
 theorem preimageHomeomorph_symm_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : s × F) :
     (e.preimageHomeomorph hb).symm p = ⟨e.symm (p.1, p.2), ((e.preimageHomeomorph hb).symm p).2⟩ :=
   rfl
 #align trivialization.preimage_homeomorph_symm_apply Trivialization.preimageHomeomorph_symm_apply
 
+/- warning: trivialization.source_homeomorph_base_set_prod -> Trivialization.sourceHomeomorphBaseSetProd is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod Trivialization.sourceHomeomorphBaseSetProdₓ'. -/
 /-- The source is homeomorphic to the product of the base set with the fiber. -/
 def sourceHomeomorphBaseSetProd : e.source ≃ₜ e.baseSet × F :=
   (Homeomorph.setCongr e.source_eq).trans (e.preimageHomeomorph subset_rfl)
 #align trivialization.source_homeomorph_base_set_prod Trivialization.sourceHomeomorphBaseSetProd
 
+/- warning: trivialization.source_homeomorph_base_set_prod_apply -> Trivialization.sourceHomeomorphBaseSetProd_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_applyₓ'. -/
 @[simp]
 theorem sourceHomeomorphBaseSetProd_apply (p : e.source) :
     e.sourceHomeomorphBaseSetProd p = (⟨proj p, e.mem_source.mp p.2⟩, (e p).2) :=
   e.preimageHomeomorph_apply subset_rfl ⟨p, e.mem_source.mp p.2⟩
 #align trivialization.source_homeomorph_base_set_prod_apply Trivialization.sourceHomeomorphBaseSetProd_apply
 
+/- warning: trivialization.source_homeomorph_base_set_prod_symm_apply -> Trivialization.sourceHomeomorphBaseSetProd_symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.source_homeomorph_base_set_prod_symm_apply Trivialization.sourceHomeomorphBaseSetProd_symm_applyₓ'. -/
 @[simp]
 theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
     e.sourceHomeomorphBaseSetProd.symm p =
@@ -471,6 +865,12 @@ theorem sourceHomeomorphBaseSetProd_symm_apply (p : e.baseSet × F) :
   rfl
 #align trivialization.source_homeomorph_base_set_prod_symm_apply Trivialization.sourceHomeomorphBaseSetProd_symm_apply
 
+/- warning: trivialization.preimage_singleton_homeomorph -> Trivialization.preimageSingletonHomeomorph is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph Trivialization.preimageSingletonHomeomorphₓ'. -/
 /-- Each fiber of a trivialization is homeomorphic to the specified fiber. -/
 def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b} ≃ₜ F :=
   (e.preimageHomeomorph (Set.singleton_subset_iff.mpr hb)).trans
@@ -478,12 +878,24 @@ def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' {b}
       (Homeomorph.punitProd F))
 #align trivialization.preimage_singleton_homeomorph Trivialization.preimageSingletonHomeomorph
 
+/- warning: trivialization.preimage_singleton_homeomorph_apply -> Trivialization.preimageSingletonHomeomorph_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_applyₓ'. -/
 @[simp]
 theorem preimageSingletonHomeomorph_apply {b : B} (hb : b ∈ e.baseSet) (p : proj ⁻¹' {b}) :
     e.preimageSingletonHomeomorph hb p = (e p).2 :=
   rfl
 #align trivialization.preimage_singleton_homeomorph_apply Trivialization.preimageSingletonHomeomorph_apply
 
+/- warning: trivialization.preimage_singleton_homeomorph_symm_apply -> Trivialization.preimageSingletonHomeomorph_symm_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.preimage_singleton_homeomorph_symm_apply Trivialization.preimageSingletonHomeomorph_symm_applyₓ'. -/
 @[simp]
 theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p : F) :
     (e.preimageSingletonHomeomorph hb).symm p =
@@ -491,11 +903,23 @@ theorem preimageSingletonHomeomorph_symm_apply {b : B} (hb : b ∈ e.baseSet) (p
   rfl
 #align trivialization.preimage_singleton_homeomorph_symm_apply Trivialization.preimageSingletonHomeomorph_symm_apply
 
+/- warning: trivialization.continuous_at_proj -> Trivialization.continuousAt_proj is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.continuous_at_proj Trivialization.continuousAt_projₓ'. -/
 /-- In the domain of a bundle trivialization, the projection is continuous-/
 theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
   (e.map_proj_nhds ex).le
 #align trivialization.continuous_at_proj Trivialization.continuousAt_proj
 
+/- warning: trivialization.comp_homeomorph -> Trivialization.compHomeomorph is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.comp_homeomorph Trivialization.compHomeomorphₓ'. -/
 /-- Composition of a `trivialization` and a `homeomorph`. -/
 protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
     Trivialization F (proj ∘ h)
@@ -510,6 +934,12 @@ protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ
     simp [hp]
 #align trivialization.comp_homeomorph Trivialization.compHomeomorph
 
+/- warning: trivialization.continuous_at_of_comp_right -> Trivialization.continuousAt_of_comp_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.continuous_at_of_comp_right Trivialization.continuousAt_of_comp_rightₓ'. -/
 /-- Read off the continuity of a function `f : Z → X` at `z : Z` by transferring via a
 trivialization of `Z` containing `z`. -/
 theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z → X} {z : Z}
@@ -524,6 +954,12 @@ theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z →
     LocalHomeomorph.symm_symm]
 #align trivialization.continuous_at_of_comp_right Trivialization.continuousAt_of_comp_right
 
+/- warning: trivialization.continuous_at_of_comp_left -> Trivialization.continuousAt_of_comp_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.continuous_at_of_comp_left Trivialization.continuousAt_of_comp_leftₓ'. -/
 /-- Read off the continuity of a function `f : X → Z` at `x : X` by transferring via a
 trivialization of `Z` containing `f x`. -/
 theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z} {x : X}
@@ -538,34 +974,76 @@ theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z
 
 variable {E} (e' : Trivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
 
+/- warning: trivialization.continuous_on -> Trivialization.continuousOn is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] (e' : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)), ContinuousOn.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) _inst_4) e') (LocalEquiv.source.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e')))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.continuous_on Trivialization.continuousOnₓ'. -/
 protected theorem continuousOn : ContinuousOn e' e'.source :=
   e'.continuous_toFun
 #align trivialization.continuous_on Trivialization.continuousOn
 
+/- warning: trivialization.coe_mem_source -> Trivialization.coe_mem_source is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] (e' : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B} {y : E b}, Iff (Membership.Mem.{max u1 u3, max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) (Set.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Set.hasMem.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) ((fun (a : Type.{u3}) (b : Type.{max u1 u3}) [self : HasLiftT.{succ u3, succ (max u1 u3)} a b] => self.0) (E b) (Bundle.TotalSpace.{u1, u3} B E) (HasLiftT.mk.{succ u3, succ (max u1 u3)} (E b) (Bundle.TotalSpace.{u1, u3} B E) (CoeTCₓ.coe.{succ u3, succ (max u1 u3)} (E b) (Bundle.TotalSpace.{u1, u3} B E) (Bundle.TotalSpace.hasCoeT.{u1, u3} B E b))) y) (LocalEquiv.source.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e')))) (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e'))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.coe_mem_source Trivialization.coe_mem_sourceₓ'. -/
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align trivialization.coe_mem_source Trivialization.coe_mem_source
 
-theorem open_target : IsOpen e'.target :=
+/- warning: trivialization.open_target -> Trivialization.open_target' is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] (e' : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)), IsOpen.{max u1 u2} (Prod.{u1, u2} B F) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (LocalEquiv.target.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e')))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.open_target Trivialization.open_target'ₓ'. -/
+theorem open_target' : IsOpen e'.target :=
   by
   rw [e'.target_eq]
   exact e'.open_base_set.prod isOpen_univ
-#align trivialization.open_target Trivialization.open_target
-
+#align trivialization.open_target Trivialization.open_target'
+
+/- warning: trivialization.coe_coe_fst -> Trivialization.coe_coe_fst is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] (e' : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B} {y : E b}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e')) -> (Eq.{succ u1} B (Prod.fst.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) _inst_4) e' ((fun (a : Type.{u3}) (b : Sort.{max (succ u1) (succ u3)}) [self : HasLiftT.{succ u3, max (succ u1) (succ u3)} a b] => self.0) (E b) (Bundle.TotalSpace.{u1, u3} B E) (HasLiftT.mk.{succ u3, max (succ u1) (succ u3)} (E b) (Bundle.TotalSpace.{u1, u3} B E) (CoeTCₓ.coe.{succ u3, max (succ u1) (succ u3)} (E b) (Bundle.TotalSpace.{u1, u3} B E) (Bundle.TotalSpace.hasCoeT.{u1, u3} B E b))) y))) b)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.coe_coe_fst Trivialization.coe_coe_fstₓ'. -/
 @[simp, mfld_simps]
 theorem coe_coe_fst (hb : b ∈ e'.baseSet) : (e' y).1 = b :=
   e'.coe_fst (e'.mem_source.2 hb)
 #align trivialization.coe_coe_fst Trivialization.coe_coe_fst
 
+/- warning: trivialization.mk_mem_target -> Trivialization.mk_mem_target is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] (e' : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B} {y : F}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Prod.{u1, u2} B F) (Set.{max u1 u2} (Prod.{u1, u2} B F)) (Set.hasMem.{max u1 u2} (Prod.{u1, u2} B F)) (Prod.mk.{u1, u2} B F b y) (LocalEquiv.target.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e')))) (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e'))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.mk_mem_target Trivialization.mk_mem_targetₓ'. -/
 theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
   e'.toPretrivialization.mem_target
 #align trivialization.mk_mem_target Trivialization.mk_mem_target
 
+/- warning: trivialization.symm_apply_apply -> Trivialization.symm_apply_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.symm_apply_apply Trivialization.symm_apply_applyₓ'. -/
 theorem symm_apply_apply {x : TotalSpace E} (hx : x ∈ e'.source) :
     e'.toLocalHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 
+/- warning: trivialization.symm_coe_proj -> Trivialization.symm_coe_proj is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] {x : B} {y : F} (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) x (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (Eq.{succ u1} B (Sigma.fst.{u1, u3} B (fun (x : B) => E x) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalHomeomorph.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4) (fun (_x : LocalHomeomorph.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalHomeomorph.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4) (LocalHomeomorph.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (Prod.mk.{u1, u2} B F x y))) x)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.symm_coe_proj Trivialization.symm_coe_projₓ'. -/
 @[simp, mfld_simps]
 theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π E)) (h : x ∈ e.baseSet) :
     (e.toLocalHomeomorph.symm (x, y)).1 = x :=
@@ -576,42 +1054,86 @@ section Zero
 
 variable [∀ x, Zero (E x)]
 
+#print Trivialization.symm /-
 /-- A fiberwise inverse to `e'`. The function `F → E x` that induces a local inverse
 `B × F → total_space E` of `e'` on `e'.base_set`. It is defined to be `0` outside `e'.base_set`. -/
 protected noncomputable def symm (e : Trivialization F (π E)) (b : B) (y : F) : E b :=
   e.toPretrivialization.symm b y
 #align trivialization.symm Trivialization.symm
+-/
 
+/- warning: trivialization.symm_apply -> Trivialization.symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.symm_apply Trivialization.symm_applyₓ'. -/
 theorem symm_apply (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
 
+/- warning: trivialization.symm_apply_of_not_mem -> Trivialization.symm_apply_of_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (x : B), Zero.{u3} (E x)] (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Not (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e))) -> (forall (y : F), Eq.{succ u3} (E b) (Trivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b y) (OfNat.ofNat.{u3} (E b) 0 (OfNat.mk.{u3} (E b) 0 (Zero.zero.{u3} (E b) (_inst_5 b)))))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_5 : forall (x : B), Zero.{u1} (E x)] (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)) {b : B}, (Not (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e))) -> (forall (y : F), Eq.{succ u1} (E b) (Trivialization.symm.{u3, u2, u1} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b y) (OfNat.ofNat.{u1} (E b) 0 (Zero.toOfNat0.{u1} (E b) (_inst_5 b))))
+Case conversion may be inaccurate. Consider using '#align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_memₓ'. -/
 theorem symm_apply_of_not_mem (e : Trivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_mem
 
+/- warning: trivialization.mk_symm -> Trivialization.mk_symm is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (x : B), Zero.{u3} (E x)] (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (forall (y : F), Eq.{max (succ u1) (succ u3)} (Bundle.TotalSpace.{u1, u3} B E) (Bundle.totalSpaceMk.{u1, u3} B E b (Trivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b y)) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (LocalHomeomorph.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4) (fun (_x : LocalHomeomorph.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4) => (Prod.{u1, u2} B F) -> (Bundle.TotalSpace.{u1, u3} B E)) (LocalHomeomorph.hasCoeToFun.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4) (LocalHomeomorph.symm.{max u1 u3, max u1 u2} (Bundle.TotalSpace.{u1, u3} B E) (Prod.{u1, u2} B F) _inst_4 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) (Prod.mk.{u1, u2} B F b y)))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_5 : forall (x : B), Zero.{u1} (E x)] (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)) {b : B}, (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e)) -> (forall (y : F), Eq.{max (succ u3) (succ u1)} (Bundle.TotalSpace.{u3, u1} B E) (Bundle.totalSpaceMk.{u3, u1} B E b (Trivialization.symm.{u3, u2, u1} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b y)) (LocalHomeomorph.toFun'.{max u3 u2, max u3 u1} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) _inst_4 (LocalHomeomorph.symm.{max u3 u1, max u3 u2} (Bundle.TotalSpace.{u3, u1} B E) (Prod.{u3, u2} B F) _inst_4 (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e)) (Prod.mk.{u3, u2} B F b y)))
+Case conversion may be inaccurate. Consider using '#align trivialization.mk_symm Trivialization.mk_symmₓ'. -/
 theorem mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     totalSpaceMk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
 
+/- warning: trivialization.symm_proj_apply -> Trivialization.symm_proj_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (x : B), Zero.{u3} (E x)] (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (z : Bundle.TotalSpace.{u1, u3} B E), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) (Bundle.TotalSpace.proj.{u1, u3} B E z) (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (Eq.{succ u3} (E (Bundle.TotalSpace.proj.{u1, u3} B E z)) (Trivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e (Bundle.TotalSpace.proj.{u1, u3} B E z) (Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) _inst_4) e z))) (Sigma.snd.{u1, u3} B (fun (x : B) => E x) z))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.symm_proj_apply Trivialization.symm_proj_applyₓ'. -/
 theorem symm_proj_apply (e : Trivialization F (π E)) (z : TotalSpace E) (hz : z.proj ∈ e.baseSet) :
     e.symm z.proj (e z).2 = z.2 :=
   e.toPretrivialization.symm_proj_apply z hz
 #align trivialization.symm_proj_apply Trivialization.symm_proj_apply
 
+/- warning: trivialization.symm_apply_apply_mk -> Trivialization.symm_apply_apply_mk is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (x : B), Zero.{u3} (E x)] (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (forall (y : E b), Eq.{succ u3} (E b) (Trivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b (Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) _inst_4) e (Bundle.totalSpaceMk.{u1, u3} B E b y)))) y)
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_5 : forall (x : B), Zero.{u1} (E x)] (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)) {b : B}, (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e)) -> (forall (y : E b), Eq.{succ u1} (E b) (Trivialization.symm.{u3, u2, u1} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b (Prod.snd.{u3, u2} B F (Trivialization.toFun'.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E) _inst_4 e (Bundle.totalSpaceMk.{u3, u1} B E b y)))) y)
+Case conversion may be inaccurate. Consider using '#align trivialization.symm_apply_apply_mk Trivialization.symm_apply_apply_mkₓ'. -/
 theorem symm_apply_apply_mk (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
     e.symm b (e (totalSpaceMk b y)).2 = y :=
   e.symm_proj_apply (totalSpaceMk b y) hb
 #align trivialization.symm_apply_apply_mk Trivialization.symm_apply_apply_mk
 
+/- warning: trivialization.apply_mk_symm -> Trivialization.apply_mk_symm is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (x : B), Zero.{u3} (E x)] (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e)) -> (forall (y : F), Eq.{max (succ u1) (succ u2)} (Prod.{u1, u2} B F) (coeFn.{max (succ u1) (succ u2) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) => (Bundle.TotalSpace.{u1, u3} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E) _inst_4) e (Bundle.totalSpaceMk.{u1, u3} B E b (Trivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b y))) (Prod.mk.{u1, u2} B F b y))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_5 : forall (x : B), Zero.{u1} (E x)] (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)) {b : B}, (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e)) -> (forall (y : F), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} B F) (Trivialization.toFun'.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u1} B E) _inst_4 e (Bundle.totalSpaceMk.{u3, u1} B E b (Trivialization.symm.{u3, u2, u1} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e b y))) (Prod.mk.{u3, u2} B F b y))
+Case conversion may be inaccurate. Consider using '#align trivialization.apply_mk_symm Trivialization.apply_mk_symmₓ'. -/
 theorem apply_mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e (totalSpaceMk b (e.symm b y)) = (b, y) :=
   e.toPretrivialization.apply_mk_symm hb y
 #align trivialization.apply_mk_symm Trivialization.apply_mk_symm
 
+/- warning: trivialization.continuous_on_symm -> Trivialization.continuousOn_symm is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (x : B), Zero.{u3} (E x)] (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)), ContinuousOn.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_4 (fun (z : Prod.{u1, u2} B F) => Bundle.totalSpaceMk.{u1, u3} B E (Prod.fst.{u1, u2} B F z) (Trivialization.symm.{u1, u2, u3} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e (Prod.fst.{u1, u2} B F z) (Prod.snd.{u1, u2} B F z))) (Set.prod.{u1, u2} B F (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e) (Set.univ.{u2} F))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_5 : forall (x : B), Zero.{u1} (E x)] (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)), ContinuousOn.{max u3 u2, max u1 u3} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) _inst_4 (fun (z : Prod.{u3, u2} B F) => Bundle.totalSpaceMk.{u3, u1} B E (Prod.fst.{u3, u2} B F z) (Trivialization.symm.{u3, u2, u1} B F E _inst_1 _inst_2 _inst_4 (fun (x : B) => _inst_5 x) e (Prod.fst.{u3, u2} B F z) (Prod.snd.{u3, u2} B F z))) (Set.prod.{u3, u2} B F (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e) (Set.univ.{u2} F))
+Case conversion may be inaccurate. Consider using '#align trivialization.continuous_on_symm Trivialization.continuousOn_symmₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem continuousOn_symm (e : Trivialization F (π E)) :
@@ -630,6 +1152,7 @@ theorem continuousOn_symm (e : Trivialization F (π E)) :
 
 end Zero
 
+#print Trivialization.transFiberHomeomorph /-
 /-- If `e` is a `trivialization` of `proj : Z → B` with fiber `F` and `h` is a homeomorphism
 `F ≃ₜ F'`, then `e.trans_fiber_homeomorph h` is the trivialization of `proj` with the fiber `F'`
 that sends `p : Z` to `((e p).1, h (e p).2)`. -/
@@ -643,19 +1166,34 @@ def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization
   target_eq := by simp [e.target_eq, prod_univ, preimage_preimage]
   proj_toFun := e.proj_toFun
 #align trivialization.trans_fiber_homeomorph Trivialization.transFiberHomeomorph
+-/
 
+/- warning: trivialization.trans_fiber_homeomorph_apply -> Trivialization.transFiberHomeomorph_apply is a dubious translation:
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 @[simp]
 theorem transFiberHomeomorph_apply {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') (x : Z) : e.transFiberHomeomorph h x = ((e x).1, h (e x).2) :=
   rfl
 #align trivialization.trans_fiber_homeomorph_apply Trivialization.transFiberHomeomorph_apply
 
+#print Trivialization.coordChange /-
 /-- Coordinate transformation in the fiber induced by a pair of bundle trivializations. See also
 `trivialization.coord_change_homeomorph` for a version bundled as `F ≃ₜ F`. -/
 def coordChange (e₁ e₂ : Trivialization F proj) (b : B) (x : F) : F :=
   (e₂ <| e₁.toLocalHomeomorph.symm (b, x)).2
 #align trivialization.coord_change Trivialization.coordChange
+-/
 
+/- warning: trivialization.mk_coord_change -> Trivialization.mk_coordChange is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.mk_coord_change Trivialization.mk_coordChangeₓ'. -/
 theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
     (b, e₁.coordChange e₂ b x) = e₂ (e₁.toLocalHomeomorph.symm (b, x)) :=
@@ -666,20 +1204,44 @@ theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈
   · rwa [e₁.proj_symm_apply' h₁]
 #align trivialization.mk_coord_change Trivialization.mk_coordChange
 
+/- warning: trivialization.coord_change_apply_snd -> Trivialization.coordChange_apply_snd is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.coord_change_apply_snd Trivialization.coordChange_apply_sndₓ'. -/
 theorem coordChange_apply_snd (e₁ e₂ : Trivialization F proj) {p : Z} (h : proj p ∈ e₁.baseSet) :
     e₁.coordChange e₂ (proj p) (e₁ p).snd = (e₂ p).snd := by
   rw [coord_change, e₁.symm_apply_mk_proj (e₁.mem_source.2 h)]
 #align trivialization.coord_change_apply_snd Trivialization.coordChange_apply_snd
 
+/- warning: trivialization.coord_change_same_apply -> Trivialization.coordChange_same_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (forall (x : F), Eq.{succ u2} F (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e e b x) x)
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B}, (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (forall (x : F), Eq.{succ u2} F (Trivialization.coordChange.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e e b x) x)
+Case conversion may be inaccurate. Consider using '#align trivialization.coord_change_same_apply Trivialization.coordChange_same_applyₓ'. -/
 theorem coordChange_same_apply (e : Trivialization F proj) {b : B} (h : b ∈ e.baseSet) (x : F) :
     e.coordChange e b x = x := by rw [coord_change, e.apply_symm_apply' h]
 #align trivialization.coord_change_same_apply Trivialization.coordChange_same_apply
 
+/- warning: trivialization.coord_change_same -> Trivialization.coordChange_same is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e)) -> (Eq.{succ u2} (F -> F) (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e e b) (id.{succ u2} F))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.coord_change_same Trivialization.coordChange_sameₓ'. -/
 theorem coordChange_same (e : Trivialization F proj) {b : B} (h : b ∈ e.baseSet) :
     e.coordChange e b = id :=
   funext <| e.coordChange_same_apply h
 #align trivialization.coord_change_same Trivialization.coordChange_same
 
+/- warning: trivialization.coord_change_coord_change -> Trivialization.coordChange_coordChange is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e₁ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e₃ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) -> (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₂)) -> (forall (x : F), Eq.{succ u2} F (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₂ e₃ b (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b x)) (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₃ b x))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align trivialization.coord_change_coord_change Trivialization.coordChange_coordChangeₓ'. -/
 theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
     e₂.coordChange e₃ b (e₁.coordChange e₂ b x) = e₁.coordChange e₃ b x :=
@@ -689,6 +1251,12 @@ theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B}
   rwa [e₂.mem_source, e₁.proj_symm_apply' h₁]
 #align trivialization.coord_change_coord_change Trivialization.coordChange_coordChange
 
+/- warning: trivialization.continuous_coord_change -> Trivialization.continuous_coordChange is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e₁ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B}, (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) -> (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₂)) -> (Continuous.{u2, u2} F F _inst_2 _inst_2 (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e₁ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B}, (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) -> (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₂)) -> (Continuous.{u2, u2} F F _inst_2 _inst_2 (Trivialization.coordChange.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b))
+Case conversion may be inaccurate. Consider using '#align trivialization.continuous_coord_change Trivialization.continuous_coordChangeₓ'. -/
 theorem continuous_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : Continuous (e₁.coordChange e₂ b) :=
   by
@@ -702,6 +1270,7 @@ theorem continuous_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁
     rwa [e₂.mem_source, e₁.proj_symm_apply' h₁]
 #align trivialization.continuous_coord_change Trivialization.continuous_coordChange
 
+#print Trivialization.coordChangeHomeomorph /-
 /-- Coordinate transformation in the fiber induced by a pair of bundle trivializations,
 as a homeomorphism. -/
 protected def coordChangeHomeomorph (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
@@ -714,7 +1283,14 @@ protected def coordChangeHomeomorph (e₁ e₂ : Trivialization F proj) {b : B}
   continuous_toFun := e₁.continuous_coordChange e₂ h₁ h₂
   continuous_invFun := e₂.continuous_coordChange e₁ h₂ h₁
 #align trivialization.coord_change_homeomorph Trivialization.coordChangeHomeomorph
+-/
 
+/- warning: trivialization.coord_change_homeomorph_coe -> Trivialization.coordChangeHomeomorph_coe is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e₁ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (h₁ : Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) (h₂ : Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e₂)), Eq.{succ u2} (F -> F) (coeFn.{succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) (fun (_x : Homeomorph.{u2, u2} F F _inst_2 _inst_2) => F -> F) (Homeomorph.hasCoeToFun.{u2, u2} F F _inst_2 _inst_2) (Trivialization.coordChangeHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b h₁ h₂)) (Trivialization.coordChange.{u1, u2, u3} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b)
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e₁ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (e₂ : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) {b : B} (h₁ : Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₁)) (h₂ : Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e₂)), Eq.{succ u2} (forall (ᾰ : F), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : F) => F) ᾰ) (FunLike.coe.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F (fun (_x : F) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : F) => F) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F F (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (Homeomorph.{u2, u2} F F _inst_2 _inst_2) F F (Homeomorph.instEquivLikeHomeomorph.{u2, u2} F F _inst_2 _inst_2))) (Trivialization.coordChangeHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b h₁ h₂)) (Trivialization.coordChange.{u3, u2, u1} B F Z _inst_1 _inst_2 proj _inst_3 e₁ e₂ b)
+Case conversion may be inaccurate. Consider using '#align trivialization.coord_change_homeomorph_coe Trivialization.coordChangeHomeomorph_coeₓ'. -/
 @[simp]
 theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : ⇑(e₁.coordChangeHomeomorph e₂ h₁ h₂) = e₁.coordChange e₂ b :=
@@ -723,11 +1299,18 @@ theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h
 
 variable {F} {B' : Type _} [TopologicalSpace B']
 
+/- warning: trivialization.is_image_preimage_prod -> Trivialization.isImage_preimage_prod is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (s : Set.{u1} B), LocalHomeomorph.IsImage.{u3, max u1 u2} Z (Prod.{u1, u2} B F) _inst_3 (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e) (Set.preimage.{u3, u1} Z B proj s) (Set.prod.{u1, u2} B F s (Set.univ.{u2} F))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (s : Set.{u3} B), LocalHomeomorph.IsImage.{u1, max u3 u2} Z (Prod.{u3, u2} B F) _inst_3 (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e) (Set.preimage.{u1, u3} Z B proj s) (Set.prod.{u3, u2} B F s (Set.univ.{u2} F))
+Case conversion may be inaccurate. Consider using '#align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
     e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
 #align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prod
 
+#print Trivialization.restrOpen /-
 /-- Restrict a `trivialization` to an open set in the base. `-/
 protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s) :
     Trivialization F proj
@@ -740,15 +1323,28 @@ protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s)
   target_eq := by simp [e.target_eq, prod_univ]
   proj_toFun p hp := e.proj_toFun p hp.1
 #align trivialization.restr_open Trivialization.restrOpen
+-/
 
 section Piecewise
 
+/- warning: trivialization.frontier_preimage -> Trivialization.frontier_preimage is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u2}} {Z : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u1} Z] (e : Trivialization.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj) (s : Set.{u3} B), Eq.{succ u1} (Set.{u1} Z) (Inter.inter.{u1} (Set.{u1} Z) (Set.instInterSet.{u1} Z) (LocalEquiv.source.{u1, max u3 u2} Z (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{u1, max u3 u2} Z (Prod.{u3, u2} B F) _inst_3 (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e))) (frontier.{u1} Z _inst_3 (Set.preimage.{u1, u3} Z B proj s))) (Set.preimage.{u1, u3} Z B proj (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (Trivialization.baseSet.{u3, u2, u1} B F Z _inst_1 _inst_2 _inst_3 proj e) (frontier.{u3} B _inst_1 s)))
+Case conversion may be inaccurate. Consider using '#align trivialization.frontier_preimage Trivialization.frontier_preimageₓ'. -/
 theorem frontier_preimage (e : Trivialization F proj) (s : Set B) :
     e.source ∩ frontier (proj ⁻¹' s) = proj ⁻¹' (e.baseSet ∩ frontier s) := by
   rw [← (e.is_image_preimage_prod s).frontier.preimage_eq, frontier_prod_univ_eq,
     (e.is_image_preimage_prod _).preimage_eq, e.source_eq, preimage_inter]
 #align trivialization.frontier_preimage Trivialization.frontier_preimage
 
+/- warning: trivialization.piecewise -> Trivialization.piecewise is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align trivialization.piecewise Trivialization.piecewiseₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Given two bundle trivializations `e`, `e'` of `proj : Z → B` and a set `s : set B` such that
 the base sets of `e` and `e'` intersect `frontier s` on the same set and `e p = e' p` whenever
@@ -770,6 +1366,12 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
   proj_toFun := by rintro p (⟨he, hs⟩ | ⟨he, hs⟩) <;> simp [*]
 #align trivialization.piecewise Trivialization.piecewise
 
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+Case conversion may be inaccurate. Consider using '#align trivialization.piecewise_le_of_eq Trivialization.piecewiseLeOfEqₓ'. -/
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B`
 over a linearly ordered base `B` and a point `a ∈ e.base_set ∩ e'.base_set` such that
 `e` equals `e'` on `proj ⁻¹' {a}`, `e.piecewise_le_of_eq e' a He He' Heq` is the bundle
@@ -785,6 +1387,7 @@ noncomputable def piecewiseLeOfEq [LinearOrder B] [OrderTopology B] (e e' : Triv
     fun p hp => Heq p <| frontier_Iic_subset _ hp.2
 #align trivialization.piecewise_le_of_eq Trivialization.piecewiseLeOfEq
 
+#print Trivialization.piecewiseLe /-
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B` over a
 linearly ordered base `B` and a point `a ∈ e.base_set ∩ e'.base_set`, `e.piecewise_le e' a He He'`
 is the bundle trivialization over `set.ite (Iic a) e.base_set e'.base_set` that is equal to `e` on
@@ -800,7 +1403,14 @@ noncomputable def piecewiseLe [LinearOrder B] [OrderTopology B] (e e' : Triviali
     · simp [e.coe_fst', e'.coe_fst', *]
     · simp [e'.coord_change_apply_snd, *]
 #align trivialization.piecewise_le Trivialization.piecewiseLe
+-/
 
+/- warning: trivialization.disjoint_union -> Trivialization.disjointUnion is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e' : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj), (Disjoint.{u1} (Set.{u1} B) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} B) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} B) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} B) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} B) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} B) (Set.completeBooleanAlgebra.{u1} B)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} B) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} B) (Set.booleanAlgebra.{u1} B))) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e')) -> (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj)
+but is expected to have type
+  forall {B : Type.{u1}} {F : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {proj : Z -> B} [_inst_3 : TopologicalSpace.{u3} Z] (e : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj) (e' : Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj), (Disjoint.{u1} (Set.{u1} B) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} B) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} B) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} B) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} B) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} B) (Set.instCompleteBooleanAlgebraSet.{u1} B)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} B) (Preorder.toLE.{u1} (Set.{u1} B) (PartialOrder.toPreorder.{u1} (Set.{u1} B) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} B) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} B) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} B) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} B) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} B) (Set.instCompleteBooleanAlgebraSet.{u1} B)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} B) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} B) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} B) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} B) (Set.instCompleteBooleanAlgebraSet.{u1} B)))))) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e) (Trivialization.baseSet.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj e')) -> (Trivialization.{u1, u2, u3} B F Z _inst_1 _inst_2 _inst_3 proj)
+Case conversion may be inaccurate. Consider using '#align trivialization.disjoint_union Trivialization.disjointUnionₓ'. -/
 /-- Given two bundle trivializations `e`, `e'` over disjoint sets, `e.disjoint_union e' H` is the
 bundle trivialization over the union of the base sets that agrees with `e` and `e'` over their
 base sets. -/

bump to nightly-2023-03-08-03

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

aa586d73

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -36,13 +36,13 @@ We provide the following operations on `trivialization`s.
 ## Implementation notes
 
 Previously, in mathlib, there was a structure `topological_vector_bundle.trivialization` which
-extended another structure `topological_fibre_bundle.trivialization` by a linearity hypothesis. As
+extended another structure `topological_fiber_bundle.trivialization` by a linearity hypothesis. As
 of PR #17359, we have changed this to a single structure `trivialization` (no namespace), together
 with a mixin class `trivialization.is_linear`.
 
-This permits all the *data* of a vector bundle to be held at the level of fibre bundles, so that the
+This permits all the *data* of a vector bundle to be held at the level of fiber bundles, so that the
 same trivializations can underlie an object's structure as (say) a vector bundle over `ℂ` and as a
-vector bundle over `ℝ`, as well as its structure simply as a fibre bundle.
+vector bundle over `ℝ`, as well as its structure simply as a fiber bundle.
 
 This might be a little surprising, given the general trend of the library to ever-increased
 bundling.  But in this case the typical motivation for more bundling does not apply: there is no

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: restore simps that used to work (#12126)

Co-authored-by: Moritz Firsching <firsching@google.com>

7c5b29b7

Diff

@@ -785,10 +785,7 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
   source_eq := by simp [source_eq]
   target_eq := by simp [target_eq, prod_univ]
   proj_toFun p := by
-    rintro (⟨he, hs⟩ | ⟨he, hs⟩)
-    -- Porting note: was `<;> simp [*]`
-    · simp [piecewise_eq_of_mem _ _ _ hs, *]
-    · simp [piecewise_eq_of_not_mem _ _ _ hs, *]
+    rintro (⟨he, hs⟩ | ⟨he, hs⟩) <;> simp [*]
 #align trivialization.piecewise Trivialization.piecewise
 
 /-- Given two bundle trivializations `e`, `e'` of a topological fiber bundle `proj : Z → B`

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -300,7 +300,7 @@ variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 `proj : Z → B` with fiber `F`, as a partial homeomorphism between `Z` and `B × F` defined between
 two sets of the form `proj ⁻¹' baseSet` and `baseSet × F`, acting trivially on the first coordinate.
 -/
--- Porting note (#11215): TODO: was @[nolint has_nonempty_instance]
+-- Porting note (#5171): was @[nolint has_nonempty_instance]
 structure Trivialization (proj : Z → B) extends PartialHomeomorph Z (B × F) where
   baseSet : Set B
   open_baseSet : IsOpen baseSet

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -54,7 +54,6 @@ open TopologicalSpace Filter Set Bundle Function
 open scoped Topology Classical Bundle
 
 variable {ι : Type*} {B : Type*} {F : Type*} {E : B → Type*}
-
 variable (F) {Z : Type*} [TopologicalSpace B] [TopologicalSpace F] {proj : Z → B}
 
 /-- This structure contains the information left for a local trivialization (which is implemented

chore: classify todo porting notes (#11216)

Classifies by adding issue number #11215 to porting notes claiming "TODO".

86f95a40

Diff

@@ -90,7 +90,7 @@ lemma ext' (e e' : Pretrivialization F proj) (h₁ : e.toPartialEquiv = e'.toPar
   cases e; cases e'; congr
 #align pretrivialization.ext Pretrivialization.ext'
 
--- Porting note: todo: move `ext` here?
+-- Porting note (#11215): TODO: move `ext` here?
 lemma ext {e e' : Pretrivialization F proj} (h₁ : ∀ x, e x = e' x)
     (h₂ : ∀ x, e.toPartialEquiv.symm x = e'.toPartialEquiv.symm x) (h₃ : e.baseSet = e'.baseSet) :
     e = e' := by
@@ -301,7 +301,7 @@ variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 `proj : Z → B` with fiber `F`, as a partial homeomorphism between `Z` and `B × F` defined between
 two sets of the form `proj ⁻¹' baseSet` and `baseSet × F`, acting trivially on the first coordinate.
 -/
--- Porting note: todo: was @[nolint has_nonempty_instance]
+-- Porting note (#11215): TODO: was @[nolint has_nonempty_instance]
 structure Trivialization (proj : Z → B) extends PartialHomeomorph Z (B × F) where
   baseSet : Set B
   open_baseSet : IsOpen baseSet

style: homogenise porting notes (#11145)

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".

8be0b69c

Diff

@@ -90,7 +90,7 @@ lemma ext' (e e' : Pretrivialization F proj) (h₁ : e.toPartialEquiv = e'.toPar
   cases e; cases e'; congr
 #align pretrivialization.ext Pretrivialization.ext'
 
--- porting note: todo: move `ext` here?
+-- Porting note: todo: move `ext` here?
 lemma ext {e e' : Pretrivialization F proj} (h₁ : ∀ x, e x = e' x)
     (h₂ : ∀ x, e.toPartialEquiv.symm x = e'.toPartialEquiv.symm x) (h₃ : e.baseSet = e'.baseSet) :
     e = e' := by
@@ -301,7 +301,7 @@ variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 `proj : Z → B` with fiber `F`, as a partial homeomorphism between `Z` and `B × F` defined between
 two sets of the form `proj ⁻¹' baseSet` and `baseSet × F`, acting trivially on the first coordinate.
 -/
--- porting note: todo: was @[nolint has_nonempty_instance]
+-- Porting note: todo: was @[nolint has_nonempty_instance]
 structure Trivialization (proj : Z → B) extends PartialHomeomorph Z (B × F) where
   baseSet : Set B
   open_baseSet : IsOpen baseSet
@@ -787,7 +787,7 @@ noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
   target_eq := by simp [target_eq, prod_univ]
   proj_toFun p := by
     rintro (⟨he, hs⟩ | ⟨he, hs⟩)
-    -- porting note: was `<;> simp [*]`
+    -- Porting note: was `<;> simp [*]`
     · simp [piecewise_eq_of_mem _ _ _ hs, *]
     · simp [piecewise_eq_of_not_mem _ _ _ hs, *]
 #align trivialization.piecewise Trivialization.piecewise

chore: reduce imports (#9830)

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

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

f4c4ca61

Diff

@@ -4,8 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Mathlib.Data.Bundle
-import Mathlib.Topology.Algebra.Order.Field
+import Mathlib.Data.Set.Image
 import Mathlib.Topology.PartialHomeomorph
+import Mathlib.Topology.Order.Basic
 
 #align_import topology.fiber_bundle.trivialization from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"

chore(Topology): remove autoImplicit in some files (#9689)

... where this is easy to do.

Co-authored-by: grunweg <grunweg@posteo.de>

9410c2d8

Diff

@@ -48,9 +48,6 @@ Indeed, since trivializations only have meaning on their base sets (taking junk
 type of linear trivializations is not even particularly well-behaved.
 -/
 
-set_option autoImplicit true
-
-
 open TopologicalSpace Filter Set Bundle Function
 
 open scoped Topology Classical Bundle
@@ -458,7 +455,7 @@ theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     ⟨e.invFun p, mem_preimage.mpr ((e.proj_symm_apply hp').symm ▸ hp.1), e.apply_symm_apply hp'⟩
 #align trivialization.image_preimage_eq_prod_univ Trivialization.image_preimage_eq_prod_univ
 
-theorem tendsto_nhds_iff {l : Filter α} {f : α → Z} {z : Z} (hz : z ∈ e.source) :
+theorem tendsto_nhds_iff {α : Type*} {l : Filter α} {f : α → Z} {z : Z} (hz : z ∈ e.source) :
     Tendsto f l (𝓝 z) ↔
       Tendsto (proj ∘ f) l (𝓝 (proj z)) ∧ Tendsto (fun x ↦ (e (f x)).2) l (𝓝 (e z).2) := by
   rw [e.nhds_eq_comap_inf_principal hz, tendsto_inf, tendsto_comap_iff, Prod.tendsto_iff, coe_coe,

chore: audit remaining uses of "local homeomorphism" in comments (#9245)

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.

a76fbc3d

Diff

@@ -16,10 +16,10 @@ import Mathlib.Topology.PartialHomeomorph
 
 ### Basic definitions
 
-* `Trivialization F p` : structure extending local homeomorphisms, defining a local
+* `Trivialization F p` : structure extending partial homeomorphisms, defining a local
   trivialization of a topological space `Z` with projection `p` and fiber `F`.
 
-* `Pretrivialization F proj` : trivialization as a local equivalence, mainly used when the
+* `Pretrivialization F proj` : trivialization as a partial equivalence, mainly used when the
   topology on the total space has not yet been defined.
 
 ### Operations on bundles
@@ -299,9 +299,9 @@ end Pretrivialization
 
 variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 
-/-- A structure extending local homeomorphisms, defining a local trivialization of a projection
-`proj : Z → B` with fiber `F`, as a local homeomorphism between `Z` and `B × F` defined between two
-sets of the form `proj ⁻¹' baseSet` and `baseSet × F`, acting trivially on the first coordinate.
+/-- A structure extending partial homeomorphisms, defining a local trivialization of a projection
+`proj : Z → B` with fiber `F`, as a partial homeomorphism between `Z` and `B × F` defined between
+two sets of the form `proj ⁻¹' baseSet` and `baseSet × F`, acting trivially on the first coordinate.
 -/
 -- porting note: todo: was @[nolint has_nonempty_instance]
 structure Trivialization (proj : Z → B) extends PartialHomeomorph Z (B × F) where

chore: rename LocalEquiv to PartialEquiv (#8984)

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>

f7006a73

Diff

@@ -64,7 +64,7 @@ below as `Trivialization F proj`) if the total space has not been given a topolo
 have a topology on both the fiber and the base space. Through the construction
 `topological_fiber_prebundle F proj` it will be possible to promote a
 `Pretrivialization F proj` to a `Trivialization F proj`. -/
-structure Pretrivialization (proj : Z → B) extends LocalEquiv Z (B × F) where
+structure Pretrivialization (proj : Z → B) extends PartialEquiv Z (B × F) where
   open_target : IsOpen target
   baseSet : Set B
   open_baseSet : IsOpen baseSet
@@ -79,37 +79,37 @@ variable {F}
 variable (e : Pretrivialization F proj) {x : Z}
 
 /-- Coercion of a pretrivialization to a function. We don't use `e.toFun` in the `CoeFun` instance
-because it is actually `e.toLocalEquiv.toFun`, so `simp` will apply lemmas about
-`toLocalEquiv`. While we may want to switch to this behavior later, doing it mid-port will break a
+because it is actually `e.toPartialEquiv.toFun`, so `simp` will apply lemmas about
+`toPartialEquiv`. While we may want to switch to this behavior later, doing it mid-port will break a
 lot of proofs.  -/
 @[coe] def toFun' : Z → (B × F) := e.toFun
 
 instance : CoeFun (Pretrivialization F proj) fun _ => Z → B × F := ⟨toFun'⟩
 
 @[ext]
-lemma ext' (e e' : Pretrivialization F proj) (h₁ : e.toLocalEquiv = e'.toLocalEquiv)
+lemma ext' (e e' : Pretrivialization F proj) (h₁ : e.toPartialEquiv = e'.toPartialEquiv)
     (h₂ : e.baseSet = e'.baseSet) : e = e' := by
   cases e; cases e'; congr
 #align pretrivialization.ext Pretrivialization.ext'
 
 -- porting note: todo: move `ext` here?
 lemma ext {e e' : Pretrivialization F proj} (h₁ : ∀ x, e x = e' x)
-    (h₂ : ∀ x, e.toLocalEquiv.symm x = e'.toLocalEquiv.symm x) (h₃ : e.baseSet = e'.baseSet) :
+    (h₂ : ∀ x, e.toPartialEquiv.symm x = e'.toPartialEquiv.symm x) (h₃ : e.baseSet = e'.baseSet) :
     e = e' := by
   ext1 <;> [ext1; exact h₃]
   · apply h₁
   · apply h₂
   · rw [e.source_eq, e'.source_eq, h₃]
 
-/-- If the fiber is nonempty, then the projection to -/
-lemma toLocalEquiv_injective [Nonempty F] :
-    Injective (toLocalEquiv : Pretrivialization F proj → LocalEquiv Z (B × F)) := fun e e' h => by
-  refine ext' _ _ h ?_
+/-- If the fiber is nonempty, then the projection also is. -/
+lemma toPartialEquiv_injective [Nonempty F] :
+    Injective (toPartialEquiv : Pretrivialization F proj → PartialEquiv Z (B × F)) := by
+  refine fun e e' h ↦ ext' _ _ h ?_
   simpa only [fst_image_prod, univ_nonempty, target_eq]
-    using congr_arg (Prod.fst '' LocalEquiv.target ·) h
+    using congr_arg (Prod.fst '' PartialEquiv.target ·) h
 
 @[simp, mfld_simps]
-theorem coe_coe : ⇑e.toLocalEquiv = e :=
+theorem coe_coe : ⇑e.toPartialEquiv = e :=
   rfl
 #align pretrivialization.coe_coe Pretrivialization.coe_coe
 
@@ -138,91 +138,91 @@ theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
 
 /-- Composition of inverse and coercion from the subtype of the target. -/
 def setSymm : e.target → Z :=
-  e.target.restrict e.toLocalEquiv.symm
+  e.target.restrict e.toPartialEquiv.symm
 #align pretrivialization.set_symm Pretrivialization.setSymm
 
 theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet := by
   rw [e.target_eq, prod_univ, mem_preimage]
 #align pretrivialization.mem_target Pretrivialization.mem_target
 
-theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalEquiv.symm x) = x.1 := by
+theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toPartialEquiv.symm x) = x.1 := by
   have := (e.coe_fst (e.map_target hx)).symm
   rwa [← e.coe_coe, e.right_inv hx] at this
 #align pretrivialization.proj_symm_apply Pretrivialization.proj_symm_apply
 
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    proj (e.toLocalEquiv.symm (b, x)) = b :=
+    proj (e.toPartialEquiv.symm (b, x)) = b :=
   e.proj_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.proj_symm_apply' Pretrivialization.proj_symm_apply'
 
 theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet := fun b hb =>
   let ⟨y⟩ := ‹Nonempty F›
-  ⟨e.toLocalEquiv.symm (b, y), e.toLocalEquiv.map_target <| e.mem_target.2 hb,
+  ⟨e.toPartialEquiv.symm (b, y), e.toPartialEquiv.map_target <| e.mem_target.2 hb,
     e.proj_symm_apply' hb⟩
 #align pretrivialization.proj_surj_on_base_set Pretrivialization.proj_surjOn_baseSet
 
-theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalEquiv.symm x) = x :=
-  e.toLocalEquiv.right_inv hx
+theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toPartialEquiv.symm x) = x :=
+  e.toPartialEquiv.right_inv hx
 #align pretrivialization.apply_symm_apply Pretrivialization.apply_symm_apply
 
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    e (e.toLocalEquiv.symm (b, x)) = (b, x) :=
+    e (e.toPartialEquiv.symm (b, x)) = (b, x) :=
   e.apply_symm_apply (e.mem_target.2 hx)
 #align pretrivialization.apply_symm_apply' Pretrivialization.apply_symm_apply'
 
-theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toLocalEquiv.symm (e x) = x :=
-  e.toLocalEquiv.left_inv hx
+theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toPartialEquiv.symm (e x) = x :=
+  e.toPartialEquiv.left_inv hx
 #align pretrivialization.symm_apply_apply Pretrivialization.symm_apply_apply
 
 @[simp, mfld_simps]
 theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
-    e.toLocalEquiv.symm (proj x, (e x).2) = x := by
+    e.toPartialEquiv.symm (proj x, (e x).2) = x := by
   rw [← e.coe_fst ex, ← e.coe_coe, e.left_inv ex]
 #align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_proj
 
 @[simp, mfld_simps]
 theorem preimage_symm_proj_baseSet :
-    e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target := by
+    e.toPartialEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target := by
   refine' inter_eq_right.mpr fun x hx => _
-  simp only [mem_preimage, LocalEquiv.invFun_as_coe, e.proj_symm_apply hx]
+  simp only [mem_preimage, PartialEquiv.invFun_as_coe, e.proj_symm_apply hx]
   exact e.mem_target.mp hx
 #align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSet
 
 @[simp, mfld_simps]
 theorem preimage_symm_proj_inter (s : Set B) :
-    e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' s) ∩ e.baseSet ×ˢ univ = (s ∩ e.baseSet) ×ˢ univ := by
+    e.toPartialEquiv.symm ⁻¹' (proj ⁻¹' s) ∩ e.baseSet ×ˢ univ = (s ∩ e.baseSet) ×ˢ univ := by
   ext ⟨x, y⟩
-  suffices x ∈ e.baseSet → (proj (e.toLocalEquiv.symm (x, y)) ∈ s ↔ x ∈ s) by
+  suffices x ∈ e.baseSet → (proj (e.toPartialEquiv.symm (x, y)) ∈ s ↔ x ∈ s) by
     simpa only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ, and_congr_left_iff]
   intro h
   rw [e.proj_symm_apply' h]
 #align pretrivialization.preimage_symm_proj_inter Pretrivialization.preimage_symm_proj_inter
 
 theorem target_inter_preimage_symm_source_eq (e f : Pretrivialization F proj) :
-    f.target ∩ f.toLocalEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
+    f.target ∩ f.toPartialEquiv.symm ⁻¹' e.source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
   rw [inter_comm, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]
 #align pretrivialization.target_inter_preimage_symm_source_eq Pretrivialization.target_inter_preimage_symm_source_eq
 
 theorem trans_source (e f : Pretrivialization F proj) :
-    (f.toLocalEquiv.symm.trans e.toLocalEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
-  rw [LocalEquiv.trans_source, LocalEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
+    (f.toPartialEquiv.symm.trans e.toPartialEquiv).source = (e.baseSet ∩ f.baseSet) ×ˢ univ := by
+  rw [PartialEquiv.trans_source, PartialEquiv.symm_source, e.target_inter_preimage_symm_source_eq]
 #align pretrivialization.trans_source Pretrivialization.trans_source
 
 theorem symm_trans_symm (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm
-      = e'.toLocalEquiv.symm.trans e.toLocalEquiv := by
-  rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).symm
+      = e'.toPartialEquiv.symm.trans e.toPartialEquiv := by
+  rw [PartialEquiv.trans_symm_eq_symm_trans_symm, PartialEquiv.symm_symm]
 #align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symm
 
 theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
-  rw [LocalEquiv.trans_source, e'.source_eq, LocalEquiv.symm_source, e.target_eq, inter_comm,
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
+  rw [PartialEquiv.trans_source, e'.source_eq, PartialEquiv.symm_source, e.target_eq, inter_comm,
     e.preimage_symm_proj_inter, inter_comm]
 #align pretrivialization.symm_trans_source_eq Pretrivialization.symm_trans_source_eq
 
 theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
-  rw [← LocalEquiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ := by
+  rw [← PartialEquiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
 #align pretrivialization.symm_trans_target_eq Pretrivialization.symm_trans_target_eq
 
 variable (e' : Pretrivialization F (π F E)) {x' : TotalSpace F E} {b : B} {y : E b}
@@ -242,7 +242,7 @@ theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSe
 #align pretrivialization.mk_mem_target Pretrivialization.mk_mem_target
 
 theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π F E)) (h : x ∈ e'.baseSet) :
-    (e'.toLocalEquiv.symm (x, y)).1 = x :=
+    (e'.toPartialEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
 #align pretrivialization.symm_coe_proj Pretrivialization.symm_coe_proj
 
@@ -254,12 +254,12 @@ variable [∀ x, Zero (E x)]
 `B × F → TotalSpace F E` of `e` on `e.baseSet`. It is defined to be `0` outside `e.baseSet`. -/
 protected noncomputable def symm (e : Pretrivialization F (π F E)) (b : B) (y : F) : E b :=
   if hb : b ∈ e.baseSet then
-    cast (congr_arg E (e.proj_symm_apply' hb)) (e.toLocalEquiv.symm (b, y)).2
+    cast (congr_arg E (e.proj_symm_apply' hb)) (e.toPartialEquiv.symm (b, y)).2
   else 0
 #align pretrivialization.symm Pretrivialization.symm
 
 theorem symm_apply (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
+    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toPartialEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
 
@@ -274,7 +274,7 @@ theorem coe_symm_of_not_mem (e : Pretrivialization F (π F E)) {b : B} (hb : b 
 #align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_mem
 
 theorem mk_symm (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    TotalSpace.mk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
+    TotalSpace.mk b (e.symm b y) = e.toPartialEquiv.symm (b, y) := by
   simp only [e.symm_apply hb, TotalSpace.mk_cast (e.proj_symm_apply' hb), TotalSpace.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
 
@@ -324,8 +324,8 @@ lemma ext' (e e' : Trivialization F proj) (h₁ : e.toPartialHomeomorph = e'.toP
 #align trivialization.ext Trivialization.ext'
 
 /-- Coercion of a trivialization to a function. We don't use `e.toFun` in the `CoeFun` instance
-because it is actually `e.toLocalEquiv.toFun`, so `simp` will apply lemmas about
-`toLocalEquiv`. While we may want to switch to this behavior later, doing it mid-port will break a
+because it is actually `e.toPartialEquiv.toFun`, so `simp` will apply lemmas about
+`toPartialEquiv`. While we may want to switch to this behavior later, doing it mid-port will break a
 lot of proofs.  -/
 @[coe] def toFun' : Z → (B × F) := e.toFun
 
@@ -342,7 +342,7 @@ instance : Coe (Trivialization F proj) (Pretrivialization F proj) :=
 theorem toPretrivialization_injective :
     Function.Injective fun e : Trivialization F proj => e.toPretrivialization := fun e e' h => by
   ext1
-  exacts [PartialHomeomorph.toLocalEquiv_injective (congr_arg Pretrivialization.toLocalEquiv h),
+  exacts [PartialHomeomorph.toPartialEquiv_injective (congr_arg Pretrivialization.toPartialEquiv h),
     congr_arg Pretrivialization.baseSet h]
 #align trivialization.to_pretrivialization_injective Trivialization.toPretrivialization_injective
 
@@ -422,12 +422,12 @@ theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toPartialHomeomorph.symm (p
 #align trivialization.symm_apply_mk_proj Trivialization.symm_apply_mk_proj
 
 theorem symm_trans_source_eq (e e' : Trivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).source = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_source_eq e.toPretrivialization e'
 #align trivialization.symm_trans_source_eq Trivialization.symm_trans_source_eq
 
 theorem symm_trans_target_eq (e e' : Trivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
+    (e.toPartialEquiv.symm.trans e'.toPartialEquiv).target = (e.baseSet ∩ e'.baseSet) ×ˢ univ :=
   Pretrivialization.symm_trans_target_eq e.toPretrivialization e'
 #align trivialization.symm_trans_target_eq Trivialization.symm_trans_target_eq
 
@@ -556,9 +556,9 @@ protected def compHomeomorph {Z' : Type*} [TopologicalSpace Z'] (h : Z' ≃ₜ Z
 trivialization of `Z` containing `z`. -/
 theorem continuousAt_of_comp_right {X : Type*} [TopologicalSpace X] {f : Z → X} {z : Z}
     (e : Trivialization F proj) (he : proj z ∈ e.baseSet)
-    (hf : ContinuousAt (f ∘ e.toLocalEquiv.symm) (e z)) : ContinuousAt f z := by
-  have hez : z ∈ e.toLocalEquiv.symm.target := by
-    rw [LocalEquiv.symm_target, e.mem_source]
+    (hf : ContinuousAt (f ∘ e.toPartialEquiv.symm) (e z)) : ContinuousAt f z := by
+  have hez : z ∈ e.toPartialEquiv.symm.target := by
+    rw [PartialEquiv.symm_target, e.mem_source]
     exact he
   rwa [e.toPartialHomeomorph.symm.continuousAt_iff_continuousAt_comp_right hez,
     PartialHomeomorph.symm_symm]
@@ -600,7 +600,7 @@ theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
 
 theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
     e'.toPartialHomeomorph.symm (e' x) = x :=
-  e'.toLocalEquiv.left_inv hx
+  e'.toPartialEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 
 @[simp, mfld_simps]

chore: rename LocalHomeomorph to PartialHomeomorph (#8982)

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

bbc6e56d

Diff

@@ -5,7 +5,7 @@ Authors: Sébastien Gouëzel
 -/
 import Mathlib.Data.Bundle
 import Mathlib.Topology.Algebra.Order.Field
-import Mathlib.Topology.LocalHomeomorph
+import Mathlib.Topology.PartialHomeomorph
 
 #align_import topology.fiber_bundle.trivialization from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
 
@@ -304,12 +304,12 @@ variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 sets of the form `proj ⁻¹' baseSet` and `baseSet × F`, acting trivially on the first coordinate.
 -/
 -- porting note: todo: was @[nolint has_nonempty_instance]
-structure Trivialization (proj : Z → B) extends LocalHomeomorph Z (B × F) where
+structure Trivialization (proj : Z → B) extends PartialHomeomorph Z (B × F) where
   baseSet : Set B
   open_baseSet : IsOpen baseSet
   source_eq : source = proj ⁻¹' baseSet
   target_eq : target = baseSet ×ˢ univ
-  proj_toFun : ∀ p ∈ source, (toLocalHomeomorph p).1 = proj p
+  proj_toFun : ∀ p ∈ source, (toPartialHomeomorph p).1 = proj p
 #align trivialization Trivialization
 
 namespace Trivialization
@@ -318,7 +318,7 @@ variable {F}
 variable (e : Trivialization F proj) {x : Z}
 
 @[ext]
-lemma ext' (e e' : Trivialization F proj) (h₁ : e.toLocalHomeomorph = e'.toLocalHomeomorph)
+lemma ext' (e e' : Trivialization F proj) (h₁ : e.toPartialHomeomorph = e'.toPartialHomeomorph)
     (h₂ : e.baseSet = e'.baseSet) : e = e' := by
   cases e; cases e'; congr
 #align trivialization.ext Trivialization.ext'
@@ -342,12 +342,12 @@ instance : Coe (Trivialization F proj) (Pretrivialization F proj) :=
 theorem toPretrivialization_injective :
     Function.Injective fun e : Trivialization F proj => e.toPretrivialization := fun e e' h => by
   ext1
-  exacts [LocalHomeomorph.toLocalEquiv_injective (congr_arg Pretrivialization.toLocalEquiv h),
+  exacts [PartialHomeomorph.toLocalEquiv_injective (congr_arg Pretrivialization.toLocalEquiv h),
     congr_arg Pretrivialization.baseSet h]
 #align trivialization.to_pretrivialization_injective Trivialization.toPretrivialization_injective
 
 @[simp, mfld_simps]
-theorem coe_coe : ⇑e.toLocalHomeomorph = e :=
+theorem coe_coe : ⇑e.toPartialHomeomorph = e :=
   rfl
 #align trivialization.coe_coe Trivialization.coe_coe
 
@@ -376,11 +376,11 @@ theorem mk_proj_snd' (ex : proj x ∈ e.baseSet) : (proj x, (e x).2) = e x :=
 
 theorem source_inter_preimage_target_inter (s : Set (B × F)) :
     e.source ∩ e ⁻¹' (e.target ∩ s) = e.source ∩ e ⁻¹' s :=
-  e.toLocalHomeomorph.source_inter_preimage_target_inter s
+  e.toPartialHomeomorph.source_inter_preimage_target_inter s
 #align trivialization.source_inter_preimage_target_inter Trivialization.source_inter_preimage_target_inter
 
 @[simp, mfld_simps]
-theorem coe_mk (e : LocalHomeomorph Z (B × F)) (i j k l m) (x : Z) :
+theorem coe_mk (e : PartialHomeomorph Z (B × F)) (i j k l m) (x : Z) :
     (Trivialization.mk e i j k l m : Trivialization F proj) x = e x :=
   rfl
 #align trivialization.coe_mk Trivialization.coe_mk
@@ -389,16 +389,17 @@ theorem mem_target {x : B × F} : x ∈ e.target ↔ x.1 ∈ e.baseSet :=
   e.toPretrivialization.mem_target
 #align trivialization.mem_target Trivialization.mem_target
 
-theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toLocalHomeomorph.symm x ∈ e.source :=
-  e.toLocalHomeomorph.map_target hx
+theorem map_target {x : B × F} (hx : x ∈ e.target) : e.toPartialHomeomorph.symm x ∈ e.source :=
+  e.toPartialHomeomorph.map_target hx
 #align trivialization.map_target Trivialization.map_target
 
-theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) : proj (e.toLocalHomeomorph.symm x) = x.1 :=
+theorem proj_symm_apply {x : B × F} (hx : x ∈ e.target) :
+    proj (e.toPartialHomeomorph.symm x) = x.1 :=
   e.toPretrivialization.proj_symm_apply hx
 #align trivialization.proj_symm_apply Trivialization.proj_symm_apply
 
 theorem proj_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    proj (e.toLocalHomeomorph.symm (b, x)) = b :=
+    proj (e.toPartialHomeomorph.symm (b, x)) = b :=
   e.toPretrivialization.proj_symm_apply' hx
 #align trivialization.proj_symm_apply' Trivialization.proj_symm_apply'
 
@@ -406,17 +407,17 @@ theorem proj_surjOn_baseSet [Nonempty F] : Set.SurjOn proj e.source e.baseSet :=
   e.toPretrivialization.proj_surjOn_baseSet
 #align trivialization.proj_surj_on_base_set Trivialization.proj_surjOn_baseSet
 
-theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toLocalHomeomorph.symm x) = x :=
-  e.toLocalHomeomorph.right_inv hx
+theorem apply_symm_apply {x : B × F} (hx : x ∈ e.target) : e (e.toPartialHomeomorph.symm x) = x :=
+  e.toPartialHomeomorph.right_inv hx
 #align trivialization.apply_symm_apply Trivialization.apply_symm_apply
 
 theorem apply_symm_apply' {b : B} {x : F} (hx : b ∈ e.baseSet) :
-    e (e.toLocalHomeomorph.symm (b, x)) = (b, x) :=
+    e (e.toPartialHomeomorph.symm (b, x)) = (b, x) :=
   e.toPretrivialization.apply_symm_apply' hx
 #align trivialization.apply_symm_apply' Trivialization.apply_symm_apply'
 
 @[simp, mfld_simps]
-theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toLocalHomeomorph.symm (proj x, (e x).2) = x :=
+theorem symm_apply_mk_proj (ex : x ∈ e.source) : e.toPartialHomeomorph.symm (proj x, (e x).2) = x :=
   e.toPretrivialization.symm_apply_mk_proj ex
 #align trivialization.symm_apply_mk_proj Trivialization.symm_apply_mk_proj
 
@@ -478,7 +479,7 @@ theorem nhds_eq_inf_comap {z : Z} (hz : z ∈ e.source) :
 
 /-- The preimage of a subset of the base set is homeomorphic to the product with the fiber. -/
 def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ s × F :=
-  (e.toLocalHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
+  (e.toPartialHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)
         (e.image_preimage_eq_prod_univ hb)).trans
     ((Homeomorph.Set.prod s univ).trans ((Homeomorph.refl s).prodCongr (Homeomorph.Set.univ F)))
 #align trivialization.preimage_homeomorph Trivialization.preimageHomeomorph
@@ -541,7 +542,7 @@ theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
 /-- Composition of a `Trivialization` and a `Homeomorph`. -/
 protected def compHomeomorph {Z' : Type*} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
     Trivialization F (proj ∘ h) where
-  toLocalHomeomorph := h.toLocalHomeomorph.trans e.toLocalHomeomorph
+  toPartialHomeomorph := h.toPartialHomeomorph.trans e.toPartialHomeomorph
   baseSet := e.baseSet
   open_baseSet := e.open_baseSet
   source_eq := by simp [source_eq, preimage_preimage, (· ∘ ·)]
@@ -559,8 +560,8 @@ theorem continuousAt_of_comp_right {X : Type*} [TopologicalSpace X] {f : Z → X
   have hez : z ∈ e.toLocalEquiv.symm.target := by
     rw [LocalEquiv.symm_target, e.mem_source]
     exact he
-  rwa [e.toLocalHomeomorph.symm.continuousAt_iff_continuousAt_comp_right hez,
-    LocalHomeomorph.symm_symm]
+  rwa [e.toPartialHomeomorph.symm.continuousAt_iff_continuousAt_comp_right hez,
+    PartialHomeomorph.symm_symm]
 #align trivialization.continuous_at_of_comp_right Trivialization.continuousAt_of_comp_right
 
 /-- Read off the continuity of a function `f : X → Z` at `x : X` by transferring via a
@@ -584,7 +585,7 @@ theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align trivialization.coe_mem_source Trivialization.coe_mem_source
 
-@[deprecated LocalHomeomorph.open_target]
+@[deprecated PartialHomeomorph.open_target]
 theorem open_target' : IsOpen e'.target := e'.open_target
 #align trivialization.open_target Trivialization.open_target'
 
@@ -598,13 +599,13 @@ theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
 #align trivialization.mk_mem_target Trivialization.mk_mem_target
 
 theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
-    e'.toLocalHomeomorph.symm (e' x) = x :=
+    e'.toPartialHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 
 @[simp, mfld_simps]
 theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π F E)) (h : x ∈ e.baseSet) :
-    (e.toLocalHomeomorph.symm (x, y)).1 = x :=
+    (e.toPartialHomeomorph.symm (x, y)).1 = x :=
   e.proj_symm_apply' h
 #align trivialization.symm_coe_proj Trivialization.symm_coe_proj
 
@@ -619,7 +620,7 @@ protected noncomputable def symm (e : Trivialization F (π F E)) (b : B) (y : F)
 #align trivialization.symm Trivialization.symm
 
 theorem symm_apply (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
+    e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toPartialHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
 
@@ -629,7 +630,7 @@ theorem symm_apply_of_not_mem (e : Trivialization F (π F E)) {b : B} (hb : b 
 #align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_mem
 
 theorem mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    TotalSpace.mk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
+    TotalSpace.mk b (e.symm b y) = e.toPartialHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
 
@@ -651,12 +652,12 @@ theorem apply_mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.base
 theorem continuousOn_symm (e : Trivialization F (π F E)) :
     ContinuousOn (fun z : B × F => TotalSpace.mk' F z.1 (e.symm z.1 z.2)) (e.baseSet ×ˢ univ) := by
   have : ∀ z ∈ e.baseSet ×ˢ (univ : Set F),
-      TotalSpace.mk z.1 (e.symm z.1 z.2) = e.toLocalHomeomorph.symm z := by
+      TotalSpace.mk z.1 (e.symm z.1 z.2) = e.toPartialHomeomorph.symm z := by
     rintro x ⟨hx : x.1 ∈ e.baseSet, _⟩
     rw [e.mk_symm hx]
   refine' ContinuousOn.congr _ this
   rw [← e.target_eq]
-  exact e.toLocalHomeomorph.continuousOn_symm
+  exact e.toPartialHomeomorph.continuousOn_symm
 #align trivialization.continuous_on_symm Trivialization.continuousOn_symm
 
 end Zero
@@ -666,7 +667,7 @@ end Zero
 that sends `p : Z` to `((e p).1, h (e p).2)`. -/
 def transFiberHomeomorph {F' : Type*} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') : Trivialization F' proj where
-  toLocalHomeomorph := e.toLocalHomeomorph.transHomeomorph <| (Homeomorph.refl _).prodCongr h
+  toPartialHomeomorph := e.toPartialHomeomorph.transHomeomorph <| (Homeomorph.refl _).prodCongr h
   baseSet := e.baseSet
   open_baseSet := e.open_baseSet
   source_eq := e.source_eq
@@ -683,12 +684,12 @@ theorem transFiberHomeomorph_apply {F' : Type*} [TopologicalSpace F'] (e : Trivi
 /-- Coordinate transformation in the fiber induced by a pair of bundle trivializations. See also
 `Trivialization.coordChangeHomeomorph` for a version bundled as `F ≃ₜ F`. -/
 def coordChange (e₁ e₂ : Trivialization F proj) (b : B) (x : F) : F :=
-  (e₂ <| e₁.toLocalHomeomorph.symm (b, x)).2
+  (e₂ <| e₁.toPartialHomeomorph.symm (b, x)).2
 #align trivialization.coord_change Trivialization.coordChange
 
 theorem mk_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) (x : F) :
-    (b, e₁.coordChange e₂ b x) = e₂ (e₁.toLocalHomeomorph.symm (b, x)) := by
+    (b, e₁.coordChange e₂ b x) = e₂ (e₁.toPartialHomeomorph.symm (b, x)) := by
   refine' Prod.ext _ rfl
   rw [e₂.coe_fst', ← e₁.coe_fst', e₁.apply_symm_apply' h₁]
   · rwa [e₁.proj_symm_apply' h₁]
@@ -718,8 +719,8 @@ theorem coordChange_coordChange (e₁ e₂ e₃ : Trivialization F proj) {b : B}
 
 theorem continuous_coordChange (e₁ e₂ : Trivialization F proj) {b : B} (h₁ : b ∈ e₁.baseSet)
     (h₂ : b ∈ e₂.baseSet) : Continuous (e₁.coordChange e₂ b) := by
-  refine' continuous_snd.comp (e₂.toLocalHomeomorph.continuousOn.comp_continuous
-    (e₁.toLocalHomeomorph.continuousOn_symm.comp_continuous _ _) _)
+  refine' continuous_snd.comp (e₂.toPartialHomeomorph.continuousOn.comp_continuous
+    (e₁.toPartialHomeomorph.continuousOn_symm.comp_continuous _ _) _)
   · exact continuous_const.prod_mk continuous_id
   · exact fun x => e₁.mem_target.2 h₁
   · intro x
@@ -747,13 +748,13 @@ theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h
 variable {B' : Type*} [TopologicalSpace B']
 
 theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
-    e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
+    e.toPartialHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
 #align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prod
 
 /-- Restrict a `Trivialization` to an open set in the base. -/
 protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s) :
     Trivialization F proj where
-  toLocalHomeomorph :=
+  toPartialHomeomorph :=
     ((e.isImage_preimage_prod s).symm.restr (IsOpen.inter e.open_target (hs.prod isOpen_univ))).symm
   baseSet := e.baseSet ∩ s
   open_baseSet := IsOpen.inter e.open_baseSet hs
@@ -778,8 +779,8 @@ otherwise. -/
 noncomputable def piecewise (e e' : Trivialization F proj) (s : Set B)
     (Hs : e.baseSet ∩ frontier s = e'.baseSet ∩ frontier s)
     (Heq : EqOn e e' <| proj ⁻¹' (e.baseSet ∩ frontier s)) : Trivialization F proj where
-  toLocalHomeomorph :=
-    e.toLocalHomeomorph.piecewise e'.toLocalHomeomorph (proj ⁻¹' s) (s ×ˢ univ)
+  toPartialHomeomorph :=
+    e.toPartialHomeomorph.piecewise e'.toPartialHomeomorph (proj ⁻¹' s) (s ×ˢ univ)
       (e.isImage_preimage_prod s) (e'.isImage_preimage_prod s)
       (by rw [e.frontier_preimage, e'.frontier_preimage, Hs]) (by rwa [e.frontier_preimage])
   baseSet := s.ite e.baseSet e'.baseSet
@@ -828,8 +829,8 @@ bundle trivialization over the union of the base sets that agrees with `e` and `
 base sets. -/
 noncomputable def disjointUnion (e e' : Trivialization F proj) (H : Disjoint e.baseSet e'.baseSet) :
     Trivialization F proj where
-  toLocalHomeomorph :=
-    e.toLocalHomeomorph.disjointUnion e'.toLocalHomeomorph
+  toPartialHomeomorph :=
+    e.toPartialHomeomorph.disjointUnion e'.toPartialHomeomorph
       (by
         rw [e.source_eq, e'.source_eq]
         exact H.preimage _)

chore: rename {LocalHomeomorph,ChartedSpace}.continuous_{to,inv}Fun fields to continuousOn_{to,inv}Fun (#8848)

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

d10d71d7

Diff

@@ -577,7 +577,7 @@ theorem continuousAt_of_comp_left {X : Type*} [TopologicalSpace X] {f : X → Z}
 variable (e' : Trivialization F (π F E)) {x' : TotalSpace F E} {b : B} {y : E b}
 
 protected theorem continuousOn : ContinuousOn e' e'.source :=
-  e'.continuous_toFun
+  e'.continuousOn_toFun
 #align trivialization.continuous_on Trivialization.continuousOn
 
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=

style: cleanup by putting by on the same line as := (#8407)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

5e9b46ed

Diff

@@ -209,8 +209,9 @@ theorem trans_source (e f : Pretrivialization F proj) :
 #align pretrivialization.trans_source Pretrivialization.trans_source
 
 theorem symm_trans_symm (e e' : Pretrivialization F proj) :
-    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm = e'.toLocalEquiv.symm.trans e.toLocalEquiv :=
-  by rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
+    (e.toLocalEquiv.symm.trans e'.toLocalEquiv).symm
+      = e'.toLocalEquiv.symm.trans e.toLocalEquiv := by
+  rw [LocalEquiv.trans_symm_eq_symm_trans_symm, LocalEquiv.symm_symm]
 #align pretrivialization.symm_trans_symm Pretrivialization.symm_trans_symm
 
 theorem symm_trans_source_eq (e e' : Pretrivialization F proj) :

chore: Make Set/Finset lemmas match lattice lemma names (#7378)

Rename union_eq_left_iff_subset to union_eq_left to match sup_eq_left. Similarly for the right and inter versions.

aef04106

Diff

@@ -183,7 +183,7 @@ theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
 @[simp, mfld_simps]
 theorem preimage_symm_proj_baseSet :
     e.toLocalEquiv.symm ⁻¹' (proj ⁻¹' e.baseSet) ∩ e.target = e.target := by
-  refine' inter_eq_right_iff_subset.mpr fun x hx => _
+  refine' inter_eq_right.mpr fun x hx => _
   simp only [mem_preimage, LocalEquiv.invFun_as_coe, e.proj_symm_apply hx]
   exact e.mem_target.mp hx
 #align pretrivialization.preimage_symm_proj_base_set Pretrivialization.preimage_symm_proj_baseSet

chore: cleanup Mathlib.Init.Data.Prod (#6972)

Removing from Mathlib.Init.Data.Prod from the early parts of the import hierarchy.

While at it, remove unnecessary uses of Prod.mk.eta across the library.

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

b5528b3b

Diff

@@ -177,7 +177,7 @@ theorem symm_apply_apply {x : Z} (hx : x ∈ e.source) : e.toLocalEquiv.symm (e
 @[simp, mfld_simps]
 theorem symm_apply_mk_proj {x : Z} (ex : x ∈ e.source) :
     e.toLocalEquiv.symm (proj x, (e x).2) = x := by
-  rw [← e.coe_fst ex, Prod.mk.eta, ← e.coe_coe, e.left_inv ex]
+  rw [← e.coe_fst ex, ← e.coe_coe, e.left_inv ex]
 #align pretrivialization.symm_apply_mk_proj Pretrivialization.symm_apply_mk_proj
 
 @[simp, mfld_simps]

fix: disable autoImplicit globally (#6528)

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.

0c24f831

Diff

@@ -48,6 +48,8 @@ Indeed, since trivializations only have meaning on their base sets (taking junk
 type of linear trivializations is not even particularly well-behaved.
 -/
 
+set_option autoImplicit true
+
 
 open TopologicalSpace Filter Set Bundle Function

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -53,9 +53,9 @@ open TopologicalSpace Filter Set Bundle Function
 
 open scoped Topology Classical Bundle
 
-variable {ι : Type _} {B : Type _} {F : Type _} {E : B → Type _}
+variable {ι : Type*} {B : Type*} {F : Type*} {E : B → Type*}
 
-variable (F) {Z : Type _} [TopologicalSpace B] [TopologicalSpace F] {proj : Z → B}
+variable (F) {Z : Type*} [TopologicalSpace B] [TopologicalSpace F] {proj : Z → B}
 
 /-- This structure contains the information left for a local trivialization (which is implemented
 below as `Trivialization F proj`) if the total space has not been given a topology, but we
@@ -536,7 +536,7 @@ theorem continuousAt_proj (ex : x ∈ e.source) : ContinuousAt proj x :=
 #align trivialization.continuous_at_proj Trivialization.continuousAt_proj
 
 /-- Composition of a `Trivialization` and a `Homeomorph`. -/
-protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
+protected def compHomeomorph {Z' : Type*} [TopologicalSpace Z'] (h : Z' ≃ₜ Z) :
     Trivialization F (proj ∘ h) where
   toLocalHomeomorph := h.toLocalHomeomorph.trans e.toLocalHomeomorph
   baseSet := e.baseSet
@@ -550,7 +550,7 @@ protected def compHomeomorph {Z' : Type _} [TopologicalSpace Z'] (h : Z' ≃ₜ
 
 /-- Read off the continuity of a function `f : Z → X` at `z : Z` by transferring via a
 trivialization of `Z` containing `z`. -/
-theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z → X} {z : Z}
+theorem continuousAt_of_comp_right {X : Type*} [TopologicalSpace X] {f : Z → X} {z : Z}
     (e : Trivialization F proj) (he : proj z ∈ e.baseSet)
     (hf : ContinuousAt (f ∘ e.toLocalEquiv.symm) (e z)) : ContinuousAt f z := by
   have hez : z ∈ e.toLocalEquiv.symm.target := by
@@ -562,7 +562,7 @@ theorem continuousAt_of_comp_right {X : Type _} [TopologicalSpace X] {f : Z →
 
 /-- Read off the continuity of a function `f : X → Z` at `x : X` by transferring via a
 trivialization of `Z` containing `f x`. -/
-theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z} {x : X}
+theorem continuousAt_of_comp_left {X : Type*} [TopologicalSpace X] {f : X → Z} {x : X}
     (e : Trivialization F proj) (hf_proj : ContinuousAt (proj ∘ f) x) (he : proj (f x) ∈ e.baseSet)
     (hf : ContinuousAt (e ∘ f) x) : ContinuousAt f x := by
   rw [e.continuousAt_iff_continuousAt_comp_left]
@@ -661,7 +661,7 @@ end Zero
 /-- If `e` is a `Trivialization` of `proj : Z → B` with fiber `F` and `h` is a homeomorphism
 `F ≃ₜ F'`, then `e.trans_fiber_homeomorph h` is the trivialization of `proj` with the fiber `F'`
 that sends `p : Z` to `((e p).1, h (e p).2)`. -/
-def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
+def transFiberHomeomorph {F' : Type*} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') : Trivialization F' proj where
   toLocalHomeomorph := e.toLocalHomeomorph.transHomeomorph <| (Homeomorph.refl _).prodCongr h
   baseSet := e.baseSet
@@ -672,7 +672,7 @@ def transFiberHomeomorph {F' : Type _} [TopologicalSpace F'] (e : Trivialization
 #align trivialization.trans_fiber_homeomorph Trivialization.transFiberHomeomorph
 
 @[simp]
-theorem transFiberHomeomorph_apply {F' : Type _} [TopologicalSpace F'] (e : Trivialization F proj)
+theorem transFiberHomeomorph_apply {F' : Type*} [TopologicalSpace F'] (e : Trivialization F proj)
     (h : F ≃ₜ F') (x : Z) : e.transFiberHomeomorph h x = ((e x).1, h (e x).2) :=
   rfl
 #align trivialization.trans_fiber_homeomorph_apply Trivialization.transFiberHomeomorph_apply
@@ -741,7 +741,7 @@ theorem coordChangeHomeomorph_coe (e₁ e₂ : Trivialization F proj) {b : B} (h
   rfl
 #align trivialization.coord_change_homeomorph_coe Trivialization.coordChangeHomeomorph_coe
 
-variable {B' : Type _} [TopologicalSpace B']
+variable {B' : Type*} [TopologicalSpace B']
 
 theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
     e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! 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.Data.Bundle
 import Mathlib.Topology.Algebra.Order.Field
 import Mathlib.Topology.LocalHomeomorph
 
+#align_import topology.fiber_bundle.trivialization from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-!
 # Trivializations

refactor: redefine Bundle.TotalSpace (#5720)

Forward-port leanprover-community/mathlib#19221

5edb251a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -52,8 +52,9 @@ type of linear trivializations is not even particularly well-behaved.
 -/
 
 
-open TopologicalSpace Filter Set Function Bundle Topology
-open scoped Classical
+open TopologicalSpace Filter Set Bundle Function
+
+open scoped Topology Classical Bundle
 
 variable {ι : Type _} {B : Type _} {F : Type _} {E : B → Type _}
 
@@ -224,8 +225,9 @@ theorem symm_trans_target_eq (e e' : Pretrivialization F proj) :
   rw [← LocalEquiv.symm_source, symm_trans_symm, symm_trans_source_eq, inter_comm]
 #align pretrivialization.symm_trans_target_eq Pretrivialization.symm_trans_target_eq
 
-variable (e' : Pretrivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
+variable (e' : Pretrivialization F (π F E)) {x' : TotalSpace F E} {b : B} {y : E b}
 
+@[simp]
 theorem coe_mem_source : ↑y ∈ e'.source ↔ b ∈ e'.baseSet :=
   e'.mem_source
 #align pretrivialization.coe_mem_source Pretrivialization.coe_mem_source
@@ -239,7 +241,7 @@ theorem mk_mem_target {x : B} {y : F} : (x, y) ∈ e'.target ↔ x ∈ e'.baseSe
   e'.mem_target
 #align pretrivialization.mk_mem_target Pretrivialization.mk_mem_target
 
-theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π E)) (h : x ∈ e'.baseSet) :
+theorem symm_coe_proj {x : B} {y : F} (e' : Pretrivialization F (π F E)) (h : x ∈ e'.baseSet) :
     (e'.toLocalEquiv.symm (x, y)).1 = x :=
   e'.proj_symm_apply' h
 #align pretrivialization.symm_coe_proj Pretrivialization.symm_coe_proj
@@ -249,45 +251,45 @@ section Zero
 variable [∀ x, Zero (E x)]
 
 /-- A fiberwise inverse to `e`. This is the function `F → E b` that induces a local inverse
-`B × F → total_space E` of `e` on `e.baseSet`. It is defined to be `0` outside `e.baseSet`. -/
-protected noncomputable def symm (e : Pretrivialization F (π E)) (b : B) (y : F) : E b :=
+`B × F → TotalSpace F E` of `e` on `e.baseSet`. It is defined to be `0` outside `e.baseSet`. -/
+protected noncomputable def symm (e : Pretrivialization F (π F E)) (b : B) (y : F) : E b :=
   if hb : b ∈ e.baseSet then
     cast (congr_arg E (e.proj_symm_apply' hb)) (e.toLocalEquiv.symm (b, y)).2
   else 0
 #align pretrivialization.symm Pretrivialization.symm
 
-theorem symm_apply (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+theorem symm_apply (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalEquiv.symm (b, y)).2 :=
   dif_pos hb
 #align pretrivialization.symm_apply Pretrivialization.symm_apply
 
-theorem symm_apply_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
-    e.symm b y = 0 :=
+theorem symm_apply_of_not_mem (e : Pretrivialization F (π F E)) {b : B} (hb : b ∉ e.baseSet)
+    (y : F) : e.symm b y = 0 :=
   dif_neg hb
 #align pretrivialization.symm_apply_of_not_mem Pretrivialization.symm_apply_of_not_mem
 
-theorem coe_symm_of_not_mem (e : Pretrivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) :
+theorem coe_symm_of_not_mem (e : Pretrivialization F (π F E)) {b : B} (hb : b ∉ e.baseSet) :
     (e.symm b : F → E b) = 0 :=
   funext fun _ => dif_neg hb
 #align pretrivialization.coe_symm_of_not_mem Pretrivialization.coe_symm_of_not_mem
 
-theorem mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    totalSpaceMk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
-  rw [e.symm_apply hb, TotalSpace.mk_cast (e.proj_symm_apply' hb), TotalSpace.eta]
+theorem mk_symm (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    TotalSpace.mk b (e.symm b y) = e.toLocalEquiv.symm (b, y) := by
+  simp only [e.symm_apply hb, TotalSpace.mk_cast (e.proj_symm_apply' hb), TotalSpace.eta]
 #align pretrivialization.mk_symm Pretrivialization.mk_symm
 
-theorem symm_proj_apply (e : Pretrivialization F (π E)) (z : TotalSpace E)
+theorem symm_proj_apply (e : Pretrivialization F (π F E)) (z : TotalSpace F E)
     (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 := by
   rw [e.symm_apply hz, cast_eq_iff_heq, e.mk_proj_snd' hz, e.symm_apply_apply (e.mem_source.mpr hz)]
 #align pretrivialization.symm_proj_apply Pretrivialization.symm_proj_apply
 
-theorem symm_apply_apply_mk (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
-    e.symm b (e (totalSpaceMk b y)).2 = y :=
-  e.symm_proj_apply (totalSpaceMk b y) hb
+theorem symm_apply_apply_mk (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet)
+    (y : E b) : e.symm b (e ⟨b, y⟩).2 = y :=
+  e.symm_proj_apply ⟨b, y⟩ hb
 #align pretrivialization.symm_apply_apply_mk Pretrivialization.symm_apply_apply_mk
 
-theorem apply_mk_symm (e : Pretrivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e (totalSpaceMk b (e.symm b y)) = (b, y) := by
+theorem apply_mk_symm (e : Pretrivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    e ⟨b, e.symm b y⟩ = (b, y) := by
   rw [e.mk_symm hb, e.apply_symm_apply (e.mk_mem_target.mpr hb)]
 #align pretrivialization.apply_mk_symm Pretrivialization.apply_mk_symm
 
@@ -295,7 +297,7 @@ end Zero
 
 end Pretrivialization
 
-variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace E)]
+variable [TopologicalSpace Z] [TopologicalSpace (TotalSpace F E)]
 
 /-- A structure extending local homeomorphisms, defining a local trivialization of a projection
 `proj : Z → B` with fiber `F`, as a local homeomorphism between `Z` and `B × F` defined between two
@@ -572,7 +574,7 @@ theorem continuousAt_of_comp_left {X : Type _} [TopologicalSpace X] {f : X → Z
   exact hf_proj.preimage_mem_nhds (e.open_baseSet.mem_nhds he)
 #align trivialization.continuous_at_of_comp_left Trivialization.continuousAt_of_comp_left
 
-variable (e' : Trivialization F (π E)) {x' : TotalSpace E} {b : B} {y : E b}
+variable (e' : Trivialization F (π F E)) {x' : TotalSpace F E} {b : B} {y : E b}
 
 protected theorem continuousOn : ContinuousOn e' e'.source :=
   e'.continuous_toFun
@@ -595,13 +597,13 @@ theorem mk_mem_target {y : F} : (b, y) ∈ e'.target ↔ b ∈ e'.baseSet :=
   e'.toPretrivialization.mem_target
 #align trivialization.mk_mem_target Trivialization.mk_mem_target
 
-theorem symm_apply_apply {x : TotalSpace E} (hx : x ∈ e'.source) :
+theorem symm_apply_apply {x : TotalSpace F E} (hx : x ∈ e'.source) :
     e'.toLocalHomeomorph.symm (e' x) = x :=
   e'.toLocalEquiv.left_inv hx
 #align trivialization.symm_apply_apply Trivialization.symm_apply_apply
 
 @[simp, mfld_simps]
-theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π E)) (h : x ∈ e.baseSet) :
+theorem symm_coe_proj {x : B} {y : F} (e : Trivialization F (π F E)) (h : x ∈ e.baseSet) :
     (e.toLocalHomeomorph.symm (x, y)).1 = x :=
   e.proj_symm_apply' h
 #align trivialization.symm_coe_proj Trivialization.symm_coe_proj
@@ -611,45 +613,45 @@ section Zero
 variable [∀ x, Zero (E x)]
 
 /-- A fiberwise inverse to `e'`. The function `F → E x` that induces a local inverse
-`B × F → total_space E` of `e'` on `e'.baseSet`. It is defined to be `0` outside `e'.baseSet`. -/
-protected noncomputable def symm (e : Trivialization F (π E)) (b : B) (y : F) : E b :=
+`B × F → TotalSpace F E` of `e'` on `e'.baseSet`. It is defined to be `0` outside `e'.baseSet`. -/
+protected noncomputable def symm (e : Trivialization F (π F E)) (b : B) (y : F) : E b :=
   e.toPretrivialization.symm b y
 #align trivialization.symm Trivialization.symm
 
-theorem symm_apply (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+theorem symm_apply (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
     e.symm b y = cast (congr_arg E (e.symm_coe_proj hb)) (e.toLocalHomeomorph.symm (b, y)).2 :=
   dif_pos hb
 #align trivialization.symm_apply Trivialization.symm_apply
 
-theorem symm_apply_of_not_mem (e : Trivialization F (π E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
+theorem symm_apply_of_not_mem (e : Trivialization F (π F E)) {b : B} (hb : b ∉ e.baseSet) (y : F) :
     e.symm b y = 0 :=
   dif_neg hb
 #align trivialization.symm_apply_of_not_mem Trivialization.symm_apply_of_not_mem
 
-theorem mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    totalSpaceMk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
+theorem mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    TotalSpace.mk b (e.symm b y) = e.toLocalHomeomorph.symm (b, y) :=
   e.toPretrivialization.mk_symm hb y
 #align trivialization.mk_symm Trivialization.mk_symm
 
-theorem symm_proj_apply (e : Trivialization F (π E)) (z : TotalSpace E) (hz : z.proj ∈ e.baseSet) :
-    e.symm z.proj (e z).2 = z.2 :=
+theorem symm_proj_apply (e : Trivialization F (π F E)) (z : TotalSpace F E)
+    (hz : z.proj ∈ e.baseSet) : e.symm z.proj (e z).2 = z.2 :=
   e.toPretrivialization.symm_proj_apply z hz
 #align trivialization.symm_proj_apply Trivialization.symm_proj_apply
 
-theorem symm_apply_apply_mk (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
-    e.symm b (e (totalSpaceMk b y)).2 = y :=
-  e.symm_proj_apply (totalSpaceMk b y) hb
+theorem symm_apply_apply_mk (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : E b) :
+    e.symm b (e ⟨b, y⟩).2 = y :=
+  e.symm_proj_apply ⟨b, y⟩ hb
 #align trivialization.symm_apply_apply_mk Trivialization.symm_apply_apply_mk
 
-theorem apply_mk_symm (e : Trivialization F (π E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
-    e (totalSpaceMk b (e.symm b y)) = (b, y) :=
+theorem apply_mk_symm (e : Trivialization F (π F E)) {b : B} (hb : b ∈ e.baseSet) (y : F) :
+    e ⟨b, e.symm b y⟩ = (b, y) :=
   e.toPretrivialization.apply_mk_symm hb y
 #align trivialization.apply_mk_symm Trivialization.apply_mk_symm
 
-theorem continuousOn_symm (e : Trivialization F (π E)) :
-    ContinuousOn (fun z : B × F => totalSpaceMk z.1 (e.symm z.1 z.2)) (e.baseSet ×ˢ univ) := by
+theorem continuousOn_symm (e : Trivialization F (π F E)) :
+    ContinuousOn (fun z : B × F => TotalSpace.mk' F z.1 (e.symm z.1 z.2)) (e.baseSet ×ˢ univ) := by
   have : ∀ z ∈ e.baseSet ×ˢ (univ : Set F),
-      totalSpaceMk z.1 (e.symm z.1 z.2) = e.toLocalHomeomorph.symm z := by
+      TotalSpace.mk z.1 (e.symm z.1 z.2) = e.toLocalHomeomorph.symm z := by
     rintro x ⟨hx : x.1 ∈ e.baseSet, _⟩
     rw [e.mk_symm hx]
   refine' ContinuousOn.congr _ this

feat: add Trivialization.tendsto_nhds_iff (#5489)

This lemma generalizes FiberBundle.continuousWithinAt_totalSpace. Also add a version with equality of filters.

db4aced9

Diff

@@ -455,6 +455,25 @@ theorem image_preimage_eq_prod_univ {s : Set B} (hb : s ⊆ e.baseSet) :
     ⟨e.invFun p, mem_preimage.mpr ((e.proj_symm_apply hp').symm ▸ hp.1), e.apply_symm_apply hp'⟩
 #align trivialization.image_preimage_eq_prod_univ Trivialization.image_preimage_eq_prod_univ
 
+theorem tendsto_nhds_iff {l : Filter α} {f : α → Z} {z : Z} (hz : z ∈ e.source) :
+    Tendsto f l (𝓝 z) ↔
+      Tendsto (proj ∘ f) l (𝓝 (proj z)) ∧ Tendsto (fun x ↦ (e (f x)).2) l (𝓝 (e z).2) := by
+  rw [e.nhds_eq_comap_inf_principal hz, tendsto_inf, tendsto_comap_iff, Prod.tendsto_iff, coe_coe,
+    tendsto_principal, coe_fst _ hz]
+  by_cases hl : ∀ᶠ x in l, f x ∈ e.source
+  · simp only [hl, and_true]
+    refine (tendsto_congr' ?_).and Iff.rfl
+    exact hl.mono fun x ↦ e.coe_fst
+  · simp only [hl, and_false, false_iff, not_and]
+    rw [e.source_eq] at hl hz
+    exact fun h _ ↦ hl <| h <| e.open_baseSet.mem_nhds hz
+
+theorem nhds_eq_inf_comap {z : Z} (hz : z ∈ e.source) :
+    𝓝 z = comap proj (𝓝 (proj z)) ⊓ comap (Prod.snd ∘ e) (𝓝 (e z).2) := by
+  refine eq_of_forall_le_iff fun l ↦ ?_
+  rw [le_inf_iff, ← tendsto_iff_comap, ← tendsto_iff_comap]
+  exact e.tendsto_nhds_iff hz
+
 /-- The preimage of a subset of the base set is homeomorphic to the product with the fiber. -/
 def preimageHomeomorph {s : Set B} (hb : s ⊆ e.baseSet) : proj ⁻¹' s ≃ₜ s × F :=
   (e.toLocalHomeomorph.homeomorphOfImageSubsetSource (e.preimage_subset_source hb)

chore: fix backtick in docs (#5077)

I wrote a script to find lines that contain an odd number of backticks

878d95c4

Diff

@@ -729,7 +729,7 @@ theorem isImage_preimage_prod (e : Trivialization F proj) (s : Set B) :
     e.toLocalHomeomorph.IsImage (proj ⁻¹' s) (s ×ˢ univ) := fun x hx => by simp [e.coe_fst', hx]
 #align trivialization.is_image_preimage_prod Trivialization.isImage_preimage_prod
 
-/-- Restrict a `Trivialization` to an open set in the base. `-/
+/-- Restrict a `Trivialization` to an open set in the base. -/
 protected def restrOpen (e : Trivialization F proj) (s : Set B) (hs : IsOpen s) :
     Trivialization F proj where
   toLocalHomeomorph :=
@@ -791,7 +791,7 @@ noncomputable def piecewiseLeOfEq [LinearOrder B] [OrderTopology B] (e e' : Triv
 linearly ordered base `B` and a point `a ∈ e.baseSet ∩ e'.baseSet`, `e.piecewise_le e' a He He'`
 is the bundle trivialization over `Set.ite (Iic a) e.baseSet e'.baseSet` that is equal to `e` on
 points `p` such that `proj p ≤ a` and is equal to `((e' p).1, h (e' p).2)` otherwise, where
-`h = `e'.coord_change_homeomorph e _ _` is the homeomorphism of the fiber such that
+`h = e'.coord_change_homeomorph e _ _` is the homeomorphism of the fiber such that
 `h (e' p).2 = (e p).2` whenever `e p = a`. -/
 noncomputable def piecewiseLe [LinearOrder B] [OrderTopology B] (e e' : Trivialization F proj)
     (a : B) (He : a ∈ e.baseSet) (He' : a ∈ e'.baseSet) : Trivialization F proj :=

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -96,7 +96,7 @@ lemma ext' (e e' : Pretrivialization F proj) (h₁ : e.toLocalEquiv = e'.toLocal
 lemma ext {e e' : Pretrivialization F proj} (h₁ : ∀ x, e x = e' x)
     (h₂ : ∀ x, e.toLocalEquiv.symm x = e'.toLocalEquiv.symm x) (h₃ : e.baseSet = e'.baseSet) :
     e = e' := by
-  ext1 <;> [ext1, exact h₃]
+  ext1 <;> [ext1; exact h₃]
   · apply h₁
   · apply h₂
   · rw [e.source_eq, e'.source_eq, h₃]

chore: forward port mathlib#17611, 18742, 18198, 18520 (#3389)

SHA-only updates:

leanprover-community/mathlib#17611 – CategoryTheory.Sites.Sheaf already uses aesop_cat at this location, nothing to port.
leanprover-community/mathlib#18742 – fiber spelling, which is all of the changes to Topology.FiberBundle.Trivialization, is already in mathlib4.
leanprover-community/mathlib#18198 – FunLike change to Data.PEquiv is already in mathlib4.

Substantative forward port:

leanprover-community/mathlib#18520

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

84169f45

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.trivialization
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

chore: sync Topology/FiberBundle/Trivialization.lean (#3370)

Also fix a lean3-style name in the comment.

947fb746

Diff

@@ -36,13 +36,13 @@ We provide the following operations on `Trivialization`s.
 ## Implementation notes
 
 Previously, in mathlib, there was a structure `topological_vector_bundle.trivialization` which
-extended another structure `topological_fibre_bundle.trivialization` by a linearity hypothesis. As
+extended another structure `topological_fiber_bundle.trivialization` by a linearity hypothesis. As
 of PR leanprover-community/mathlib#17359, we have changed this to a single structure
-`Trivialization` (no namespace), together with a mixin class `trivialization.is_linear`.
+`Trivialization` (no namespace), together with a mixin class `Trivialization.IsLinear`.
 
-This permits all the *data* of a vector bundle to be held at the level of fibre bundles, so that the
+This permits all the *data* of a vector bundle to be held at the level of fiber bundles, so that the
 same trivializations can underlie an object's structure as (say) a vector bundle over `ℂ` and as a
-vector bundle over `ℝ`, as well as its structure simply as a fibre bundle.
+vector bundle over `ℝ`, as well as its structure simply as a fiber bundle.
 
 This might be a little surprising, given the general trend of the library to ever-increased
 bundling.  But in this case the typical motivation for more bundling does not apply: there is no