topology.fiber_bundle.basic ⟷ Mathlib.Topology.FiberBundle.Basic

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

@@ -913,7 +913,7 @@ variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
   [∀ x, TopologicalSpace (E x)]
 
 #print FiberPrebundle /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the local equivalences

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

@@ -399,7 +399,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
   · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
         `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
-    rw [disjoint_left] at he ; push_neg at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
+    rw [disjoint_left] at he; push_neg at he; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
     exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
 -/
@@ -504,13 +504,13 @@ def trivChange (i j : ι) : PartialHomeomorph (B × F) (B × F)
   map_target' p hp := by simpa using hp
   left_inv' := by
     rintro ⟨x, v⟩ hx
-    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx 
+    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx.1
     · simp [hx]
   right_inv' := by
     rintro ⟨x, v⟩ hx
-    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx 
+    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx.2
     · simp [hx]
@@ -552,14 +552,14 @@ def localTrivAsPartialEquiv (i : ι) : PartialEquiv Z.TotalSpace (B × F)
     simpa only [Set.mem_preimage, and_true_iff, Set.mem_univ, Set.mem_prod] using hp
   left_inv' := by
     rintro ⟨x, v⟩ hx
-    change x ∈ Z.base_set i at hx 
+    change x ∈ Z.base_set i at hx
     dsimp only
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact Z.mem_base_set_at _
     · simp only [hx, mem_inter_iff, and_self_iff, mem_base_set_at]
   right_inv' := by
     rintro ⟨x, v⟩ hx
-    simp only [prod_mk_mem_set_prod_eq, and_true_iff, mem_univ] at hx 
+    simp only [prod_mk_mem_set_prod_eq, and_true_iff, mem_univ] at hx
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx
     · simp only [hx, mem_inter_iff, and_self_iff, mem_base_set_at]
@@ -652,7 +652,7 @@ def localTriv (i : ι) : Trivialization F Z.proj
     by
     apply continuousOn_isOpen_of_generateFrom ((Z.is_open_base_set i).Prod isOpen_univ)
     intro t ht
-    simp only [exists_prop, mem_Union, mem_singleton_iff] at ht 
+    simp only [exists_prop, mem_Union, mem_singleton_iff] at ht
     obtain ⟨j, s, s_open, ts⟩ :
       ∃ j s,
         IsOpen s ∧
@@ -879,7 +879,7 @@ instance fiberBundle : FiberBundle F Z.Fiber
               _⟩
         rw [preimage_inter, ← preimage_comp, Function.comp]
         refine' ext_iff.mpr fun a => ⟨fun ha => _, fun ha => ⟨Z.mem_base_set_at b, _⟩⟩
-        · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk] at ha 
+        · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk] at ha
           exact ha.2.2
         · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk]
           exact ⟨Z.mem_base_set_at b, ha⟩⟩
@@ -997,7 +997,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       rw [isOpen_coinduced, isOpen_induced_iff]
       obtain ⟨u, hu1, hu2⟩ := continuous_on_iff'.mp (a.continuous_triv_change _ he _ he') s hs
       have hu3 := congr_arg (fun s => (fun x : e'.target => (x : B × F)) ⁻¹' s) hu2
-      simp only [Subtype.coe_preimage_self, preimage_inter, univ_inter] at hu3 
+      simp only [Subtype.coe_preimage_self, preimage_inter, univ_inter] at hu3
       refine'
         ⟨u ∩ e'.to_local_equiv.target ∩ e'.to_local_equiv.symm ⁻¹' e.source, _, by
           simp only [preimage_inter, inter_univ, Subtype.coe_preimage_self, hu3.symm]; rfl⟩
@@ -1048,7 +1048,7 @@ theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
     @Inducing _ _ _ a.totalSpaceTopology (TotalSpace.mk b) :=
   by
   letI := a.total_space_topology
-  rw [← restrict_comp_cod_restrict (a.mem_trivialization_at_source b)] at h 
+  rw [← restrict_comp_cod_restrict (a.mem_trivialization_at_source b)] at h
   apply Inducing.of_codRestrict (a.mem_trivialization_at_source b)
   refine'
     inducing_of_inducing_compose _

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

@@ -185,11 +185,11 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/

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

@@ -338,27 +338,72 @@ variable (F E)
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
     [OrderTopology B] [FiberBundle F E] (a b : B) :
-    ∃ e : Trivialization F (π F E), Icc a b ⊆ e.baseSet := by classical
+    ∃ e : Trivialization F (π F E), Icc a b ⊆ e.baseSet := by
+  classical
+  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π F E), a ∈ ea.baseSet :=
+    ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
+  -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
+    cases' le_or_lt a b with hab hab <;>
+    [skip; exact ⟨ea, by simp [*]⟩]
+  /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
+    We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
+  set s : Set B := {x ∈ Icc a b | ∃ e : Trivialization F (π F E), Icc a x ⊆ e.baseSet}
+  have ha : a ∈ s := ⟨left_mem_Icc.2 hab, ea, by simp [hea]⟩
+  have sne : s.nonempty := ⟨a, ha⟩
+  have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
+  have sbd : BddAbove s := ⟨b, hsb⟩
+  set c := Sup s
+  have hsc : IsLUB s c := isLUB_csSup sne sbd
+  have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
+  obtain ⟨-, ec : Trivialization F (π F E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
+    by
+    cases' hc.1.eq_or_lt with heq hlt; · rwa [← HEq]
+    refine' ⟨hc, _⟩
+    /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
+        of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
+    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π F E), c ∈ ec.baseSet :=
+      ⟨trivialization_at F E c, mem_base_set_trivialization_at F E c⟩
+    obtain ⟨c', hc', hc'e⟩ : ∃ c' ∈ Ico a c, Ioc c' c ⊆ ec.base_set :=
+      (mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset hlt).1
+        (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set hc)
+    /- Since `c' < c = Sup s`, there exists `d ∈ s ∩ (c', c]`. Let `ead` be a trivialization of
+        `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
+    obtain ⟨d, ⟨hdab, ead, had⟩, hd⟩ : ∃ d ∈ s, d ∈ Ioc c' c := hsc.exists_between hc'.2
+    refine' ⟨ead.piecewise_le ec d (had ⟨hdab.1, le_rfl⟩) (hc'e hd), subset_ite.2 _⟩
+    refine' ⟨fun x hx => had ⟨hx.1.1, hx.2⟩, fun x hx => hc'e ⟨hd.1.trans (not_le.1 hx.2), hx.1.2⟩⟩
+  /- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
+    done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
+    `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
+  cases' hc.2.eq_or_lt with heq hlt
+  · exact ⟨ec, HEq ▸ hec⟩
+  rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
+  · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
+  /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
+    `d ∈ (c, b]`. -/
+  obtain ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, Ico c d ⊆ ec.base_set :=
+    (mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset hlt).1
+      (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set (hec ⟨hc.1, le_rfl⟩))
+  have had : Ico a d ⊆ ec.base_set := Ico_subset_Icc_union_Ico.trans (union_subset hec hd)
+  by_cases he : Disjoint (Iio d) (Ioi c)
+  · /- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
+        Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
+        a trivialization over `[a, d]`. -/
+    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π F E), d ∈ ed.baseSet :=
+      ⟨trivialization_at F E d, mem_base_set_trivialization_at F E d⟩
+    refine'
+      ⟨d, hdcb,
+        (ec.restr_open (Iio d) isOpen_Iio).disjointUnion (ed.restr_open (Ioi c) isOpen_Ioi)
+          (he.mono (inter_subset_right _ _) (inter_subset_right _ _)),
+        fun x hx => _⟩
+    rcases hx.2.eq_or_lt with (rfl | hxd)
+    exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
+  · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
+        `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
+    rw [disjoint_left] at he ; push_neg at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
+    exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
 -/
 
--- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
-/- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
-  We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
-/- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
-    of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
-/- Since `c' < c = Sup s`, there exists `d ∈ s ∩ (c', c]`. Let `ead` be a trivialization of
-    `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
-/- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
-  done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
-  `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
-/- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
-  `d ∈ (c, b]`. -/
-/- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
-    Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
-    a trivialization over `[a, d]`. -/
-/- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
-    `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
 end FiberBundle
 
 /-! ### Core construction for constructing fiber bundles -/

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

@@ -338,72 +338,27 @@ variable (F E)
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
     [OrderTopology B] [FiberBundle F E] (a b : B) :
-    ∃ e : Trivialization F (π F E), Icc a b ⊆ e.baseSet := by
-  classical
-  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π F E), a ∈ ea.baseSet :=
-    ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
-  -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
-    cases' le_or_lt a b with hab hab <;>
-    [skip; exact ⟨ea, by simp [*]⟩]
-  /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
-    We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
-  set s : Set B := {x ∈ Icc a b | ∃ e : Trivialization F (π F E), Icc a x ⊆ e.baseSet}
-  have ha : a ∈ s := ⟨left_mem_Icc.2 hab, ea, by simp [hea]⟩
-  have sne : s.nonempty := ⟨a, ha⟩
-  have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
-  have sbd : BddAbove s := ⟨b, hsb⟩
-  set c := Sup s
-  have hsc : IsLUB s c := isLUB_csSup sne sbd
-  have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
-  obtain ⟨-, ec : Trivialization F (π F E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
-    by
-    cases' hc.1.eq_or_lt with heq hlt; · rwa [← HEq]
-    refine' ⟨hc, _⟩
-    /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
-        of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
-    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π F E), c ∈ ec.baseSet :=
-      ⟨trivialization_at F E c, mem_base_set_trivialization_at F E c⟩
-    obtain ⟨c', hc', hc'e⟩ : ∃ c' ∈ Ico a c, Ioc c' c ⊆ ec.base_set :=
-      (mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset hlt).1
-        (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set hc)
-    /- Since `c' < c = Sup s`, there exists `d ∈ s ∩ (c', c]`. Let `ead` be a trivialization of
-        `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
-    obtain ⟨d, ⟨hdab, ead, had⟩, hd⟩ : ∃ d ∈ s, d ∈ Ioc c' c := hsc.exists_between hc'.2
-    refine' ⟨ead.piecewise_le ec d (had ⟨hdab.1, le_rfl⟩) (hc'e hd), subset_ite.2 _⟩
-    refine' ⟨fun x hx => had ⟨hx.1.1, hx.2⟩, fun x hx => hc'e ⟨hd.1.trans (not_le.1 hx.2), hx.1.2⟩⟩
-  /- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
-    done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
-    `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
-  cases' hc.2.eq_or_lt with heq hlt
-  · exact ⟨ec, HEq ▸ hec⟩
-  rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
-  · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
-  /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
-    `d ∈ (c, b]`. -/
-  obtain ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, Ico c d ⊆ ec.base_set :=
-    (mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset hlt).1
-      (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set (hec ⟨hc.1, le_rfl⟩))
-  have had : Ico a d ⊆ ec.base_set := Ico_subset_Icc_union_Ico.trans (union_subset hec hd)
-  by_cases he : Disjoint (Iio d) (Ioi c)
-  · /- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
-        Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
-        a trivialization over `[a, d]`. -/
-    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π F E), d ∈ ed.baseSet :=
-      ⟨trivialization_at F E d, mem_base_set_trivialization_at F E d⟩
-    refine'
-      ⟨d, hdcb,
-        (ec.restr_open (Iio d) isOpen_Iio).disjointUnion (ed.restr_open (Ioi c) isOpen_Ioi)
-          (he.mono (inter_subset_right _ _) (inter_subset_right _ _)),
-        fun x hx => _⟩
-    rcases hx.2.eq_or_lt with (rfl | hxd)
-    exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
-  · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
-        `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
-    rw [disjoint_left] at he ; push_neg at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
-    exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
+    ∃ e : Trivialization F (π F E), Icc a b ⊆ e.baseSet := by classical
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
 -/
 
+-- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
+/- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
+  We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
+/- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
+    of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
+/- Since `c' < c = Sup s`, there exists `d ∈ s ∩ (c', c]`. Let `ead` be a trivialization of
+    `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
+/- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
+  done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
+  `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
+/- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
+  `d ∈ (c, b]`. -/
+/- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
+    Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
+    a trivialization over `[a, d]`. -/
+/- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
+    `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
 end FiberBundle
 
 /-! ### Core construction for constructing fiber bundles -/

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

@@ -185,11 +185,11 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/

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

@@ -531,7 +531,7 @@ theorem mem_trivChange_source (i j : ι) (p : B × F) :
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print FiberBundleCore.localTrivAsLocalEquiv /-
+#print FiberBundleCore.localTrivAsPartialEquiv /-
 /-- Associate to a trivialization index `i : ι` the corresponding trivialization, i.e., a bijection
 between `proj ⁻¹ (base_set i)` and `base_set i × F`. As the fiber above `x` is `F` but read in the
 chart with index `index_at x`, the trivialization in the fiber above x is by definition the
@@ -540,7 +540,7 @@ The local trivialization will ultimately be a local homeomorphism. For now, we o
 local equiv version, denoted with a prime. In further developments, avoid this auxiliary version,
 and use `Z.local_triv` instead.
 -/
-def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
+def localTrivAsPartialEquiv (i : ι) : PartialEquiv Z.TotalSpace (B × F)
     where
   source := Z.proj ⁻¹' Z.baseSet i
   target := Z.baseSet i ×ˢ univ
@@ -563,47 +563,47 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx
     · simp only [hx, mem_inter_iff, and_self_iff, mem_base_set_at]
-#align fiber_bundle_core.local_triv_as_local_equiv FiberBundleCore.localTrivAsLocalEquiv
+#align fiber_bundle_core.local_triv_as_local_equiv FiberBundleCore.localTrivAsPartialEquiv
 -/
 
 variable (i : ι)
 
-#print FiberBundleCore.mem_localTrivAsLocalEquiv_source /-
-theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
-    p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
+#print FiberBundleCore.mem_localTrivAsPartialEquiv_source /-
+theorem mem_localTrivAsPartialEquiv_source (p : Z.TotalSpace) :
+    p ∈ (Z.localTrivAsPartialEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
-#align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
+#align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsPartialEquiv_source
 -/
 
-#print FiberBundleCore.mem_localTrivAsLocalEquiv_target /-
-theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
-    p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i := by erw [mem_prod];
+#print FiberBundleCore.mem_localTrivAsPartialEquiv_target /-
+theorem mem_localTrivAsPartialEquiv_target (p : B × F) :
+    p ∈ (Z.localTrivAsPartialEquiv i).target ↔ p.1 ∈ Z.baseSet i := by erw [mem_prod];
   simp only [and_true_iff, mem_univ]
-#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_target
+#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsPartialEquiv_target
 -/
 
-#print FiberBundleCore.localTrivAsLocalEquiv_apply /-
-theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
-    (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
+#print FiberBundleCore.localTrivAsPartialEquiv_apply /-
+theorem localTrivAsPartialEquiv_apply (p : Z.TotalSpace) :
+    (Z.localTrivAsPartialEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
+#align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsPartialEquiv_apply
 -/
 
-#print FiberBundleCore.localTrivAsLocalEquiv_trans /-
+#print FiberBundleCore.localTrivAsPartialEquiv_trans /-
 /-- The composition of two local trivializations is the trivialization change Z.triv_change i j. -/
-theorem localTrivAsLocalEquiv_trans (i j : ι) :
-    (Z.localTrivAsLocalEquiv i).symm.trans (Z.localTrivAsLocalEquiv j) ≈
-      (Z.trivChange i j).toLocalEquiv :=
+theorem localTrivAsPartialEquiv_trans (i j : ι) :
+    (Z.localTrivAsPartialEquiv i).symm.trans (Z.localTrivAsPartialEquiv j) ≈
+      (Z.trivChange i j).toPartialEquiv :=
   by
   constructor
   · ext x; simp only [mem_local_triv_as_local_equiv_target, mfld_simps]; rfl
   · rintro ⟨x, v⟩ hx
-    simp only [triv_change, local_triv_as_local_equiv, LocalEquiv.symm, true_and_iff,
-      Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, LocalEquiv.trans_source, mem_inter_iff,
-      and_true_iff, mem_preimage, proj, mem_univ, LocalEquiv.coe_mk, eq_self_iff_true,
-      LocalEquiv.coe_trans, total_space.proj] at hx ⊢
+    simp only [triv_change, local_triv_as_local_equiv, PartialEquiv.symm, true_and_iff,
+      Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, PartialEquiv.trans_source, mem_inter_iff,
+      and_true_iff, mem_preimage, proj, mem_univ, PartialEquiv.coe_mk, eq_self_iff_true,
+      PartialEquiv.coe_trans, total_space.proj] at hx ⊢
     simp only [Z.coord_change_comp, hx, mem_inter_iff, and_self_iff, mem_base_set_at]
-#align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_trans
+#align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsPartialEquiv_trans
 -/
 
 #print FiberBundleCore.toTopologicalSpace /-
@@ -619,7 +619,7 @@ variable (b : B) (a : F)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print FiberBundleCore.open_source' /-
-theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
+theorem open_source' (i : ι) : IsOpen (Z.localTrivAsPartialEquiv i).source :=
   by
   apply TopologicalSpace.GenerateOpen.basic
   simp only [exists_prop, mem_Union, mem_singleton_iff]
@@ -659,7 +659,7 @@ def localTriv (i : ι) : Trivialization F Z.proj
           t = (local_triv_as_local_equiv Z j).source ∩ local_triv_as_local_equiv Z j ⁻¹' s :=
       ht
     rw [ts]
-    simp only [LocalEquiv.right_inv, preimage_inter, LocalEquiv.left_inv]
+    simp only [PartialEquiv.right_inv, preimage_inter, PartialEquiv.left_inv]
     let e := Z.local_triv_as_local_equiv i
     let e' := Z.local_triv_as_local_equiv j
     let f := e.symm.trans e'
@@ -670,10 +670,10 @@ def localTriv (i : ι) : Trivialization F Z.proj
         (continuousOn_open_iff (Z.triv_change i j).open_source).1 (Z.triv_change i j).ContinuousOn _
           s_open
     convert this using 1
-    dsimp [LocalEquiv.trans_source]
+    dsimp [PartialEquiv.trans_source]
     rw [← preimage_comp, inter_assoc]
     rfl
-  toLocalEquiv := Z.localTrivAsLocalEquiv i
+  toPartialEquiv := Z.localTrivAsPartialEquiv i
 #align fiber_bundle_core.local_triv FiberBundleCore.localTriv
 -/
 
@@ -715,35 +715,35 @@ theorem continuous_const_section (v : F)
 #align fiber_bundle_core.continuous_const_section FiberBundleCore.continuous_const_section
 -/
 
-#print FiberBundleCore.localTrivAsLocalEquiv_coe /-
+#print FiberBundleCore.localTrivAsPartialEquiv_coe /-
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv i :=
+theorem localTrivAsPartialEquiv_coe : ⇑(Z.localTrivAsPartialEquiv i) = Z.localTriv i :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsLocalEquiv_coe
+#align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsPartialEquiv_coe
 -/
 
-#print FiberBundleCore.localTrivAsLocalEquiv_source /-
+#print FiberBundleCore.localTrivAsPartialEquiv_source /-
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_source :
-    (Z.localTrivAsLocalEquiv i).source = (Z.localTriv i).source :=
+theorem localTrivAsPartialEquiv_source :
+    (Z.localTrivAsPartialEquiv i).source = (Z.localTriv i).source :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsLocalEquiv_source
+#align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsPartialEquiv_source
 -/
 
-#print FiberBundleCore.localTrivAsLocalEquiv_target /-
+#print FiberBundleCore.localTrivAsPartialEquiv_target /-
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_target :
-    (Z.localTrivAsLocalEquiv i).target = (Z.localTriv i).target :=
+theorem localTrivAsPartialEquiv_target :
+    (Z.localTrivAsPartialEquiv i).target = (Z.localTriv i).target :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsLocalEquiv_target
+#align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsPartialEquiv_target
 -/
 
-#print FiberBundleCore.localTrivAsLocalEquiv_symm /-
+#print FiberBundleCore.localTrivAsPartialEquiv_symm /-
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_symm :
-    (Z.localTrivAsLocalEquiv i).symm = (Z.localTriv i).toLocalEquiv.symm :=
+theorem localTrivAsPartialEquiv_symm :
+    (Z.localTrivAsPartialEquiv i).symm = (Z.localTriv i).toPartialEquiv.symm :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsLocalEquiv_symm
+#align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsPartialEquiv_symm
 -/
 
 #print FiberBundleCore.baseSet_at /-
@@ -926,7 +926,7 @@ structure FiberPrebundle where
   pretrivialization_mem_atlas : ∀ x : B, pretrivialization_at x ∈ pretrivialization_atlas
   continuous_triv_change :
     ∀ (e) (_ : e ∈ pretrivialization_atlas) (e') (_ : e' ∈ pretrivialization_atlas),
-      ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
+      ContinuousOn (e ∘ e'.toPartialEquiv.symm) (e'.target ∩ e'.toPartialEquiv.symm ⁻¹' e.source)
   totalSpace_mk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ TotalSpace.mk b)
 #align fiber_prebundle FiberPrebundle
 -/
@@ -945,7 +945,7 @@ def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace F
 
 #print FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas /-
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
-    @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
+    @ContinuousOn _ _ _ a.totalSpaceTopology e.toPartialEquiv.symm e.target :=
   by
   refine'
     id fun z H =>
@@ -970,7 +970,7 @@ theorem isOpen_source (e : Pretrivialization F (π F E)) : is_open[a.totalSpaceT
 #print FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter /-
 theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π F E))
     (he' : e' ∈ a.pretrivializationAtlas) :
-    IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) :=
+    IsOpen (e'.toPartialEquiv.target ∩ e'.toPartialEquiv.symm ⁻¹' e.source) :=
   by
   letI := a.total_space_topology
   obtain ⟨u, hu1, hu2⟩ :=
@@ -1100,7 +1100,7 @@ theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalS
     {s : Set B} (hs : IsOpen s)
     (hf :
       ∀ b ∈ s,
-        ContinuousOn (f ∘ (a.pretrivializationAt b).toLocalEquiv.symm)
+        ContinuousOn (f ∘ (a.pretrivializationAt b).toPartialEquiv.symm)
           ((s ∩ (a.pretrivializationAt b).baseSet) ×ˢ (Set.univ : Set F))) :
     @ContinuousOn _ _ a.totalSpaceTopology _ f (π F E ⁻¹' s) :=
   by

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

@@ -494,7 +494,7 @@ def proj : Z.TotalSpace → B :=
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print FiberBundleCore.trivChange /-
 /-- Local homeomorphism version of the trivialization change. -/
-def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
+def trivChange (i j : ι) : PartialHomeomorph (B × F) (B × F)
     where
   source := (Z.baseSet i ∩ Z.baseSet j) ×ˢ univ
   target := (Z.baseSet i ∩ Z.baseSet j) ×ˢ univ
@@ -704,7 +704,7 @@ theorem continuous_const_section (v : F)
   apply continuous_iff_continuousAt.2 fun x => _
   have A : Z.base_set (Z.index_at x) ∈ 𝓝 x :=
     IsOpen.mem_nhds (Z.is_open_base_set (Z.index_at x)) (Z.mem_base_set_at x)
-  apply ((Z.local_triv_at x).toLocalHomeomorph.continuousAt_iff_continuousAt_comp_left _).2
+  apply ((Z.local_triv_at x).toPartialHomeomorph.continuousAt_iff_continuousAt_comp_left _).2
   · simp only [(· ∘ ·), mfld_simps]
     apply continuous_at_id.prod
     have : ContinuousOn (fun y : B => v) (Z.base_set (Z.index_at x)) := continuousOn_const
@@ -819,7 +819,7 @@ theorem mem_localTrivAt_target (p : B × F) (b : B) :
 #print FiberBundleCore.localTriv_symm_apply /-
 @[simp, mfld_simps]
 theorem localTriv_symm_apply (p : B × F) :
-    (Z.localTriv i).toLocalHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
+    (Z.localTriv i).toPartialHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_apply
 -/

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

@@ -650,7 +650,7 @@ def localTriv (i : ι) : Trivialization F Z.proj
     exact ⟨i, s, s_open, rfl⟩
   continuous_invFun :=
     by
-    apply continuousOn_open_of_generateFrom ((Z.is_open_base_set i).Prod isOpen_univ)
+    apply continuousOn_isOpen_of_generateFrom ((Z.is_open_base_set i).Prod isOpen_univ)
     intro t ht
     simp only [exists_prop, mem_Union, mem_singleton_iff] at ht 
     obtain ⟨j, s, s_open, ts⟩ :

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

@@ -3,7 +3,7 @@ Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 -/
-import Mathbin.Topology.FiberBundle.Trivialization
+import Topology.FiberBundle.Trivialization
 
 #align_import topology.fiber_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
 
@@ -185,11 +185,11 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/
@@ -913,7 +913,7 @@ variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
   [∀ x, TopologicalSpace (E x)]
 
 #print FiberPrebundle /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the local equivalences

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

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
-
-! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.FiberBundle.Trivialization
 
+#align_import topology.fiber_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-!
 # Fiber bundles
 
@@ -916,7 +913,7 @@ variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
   [∀ x, TopologicalSpace (E x)]
 
 #print FiberPrebundle /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the local equivalences

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

@@ -188,7 +188,7 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpaceₓ_mk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpace_mk_inducing] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
@@ -197,7 +197,7 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/
 class FiberBundle where
-  totalSpaceₓ_mk_inducing : ∀ b : B, Inducing (@TotalSpace.mk B F E b)
+  totalSpace_mk_inducing : ∀ b : B, Inducing (@TotalSpace.mk B F E b)
   trivializationAtlas : Set (Trivialization F (π F E))
   trivializationAt : B → Trivialization F (π F E)
   mem_baseSet_trivializationAt : ∀ b : B, b ∈ (trivialization_at b).baseSet
@@ -488,7 +488,7 @@ def TotalSpace :=
 #print FiberBundleCore.proj /-
 /-- The projection from the total space of a fiber bundle core, on its base. -/
 @[reducible, simp, mfld_simps]
-def proj : Z.TotalSpaceₓ → B :=
+def proj : Z.TotalSpace → B :=
   Bundle.TotalSpace.proj
 #align fiber_bundle_core.proj FiberBundleCore.proj
 -/
@@ -543,7 +543,7 @@ The local trivialization will ultimately be a local homeomorphism. For now, we o
 local equiv version, denoted with a prime. In further developments, avoid this auxiliary version,
 and use `Z.local_triv` instead.
 -/
-def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpaceₓ (B × F)
+def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
     where
   source := Z.proj ⁻¹' Z.baseSet i
   target := Z.baseSet i ×ˢ univ
@@ -572,7 +572,7 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpaceₓ (B × F)
 variable (i : ι)
 
 #print FiberBundleCore.mem_localTrivAsLocalEquiv_source /-
-theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpaceₓ) :
+theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
@@ -586,7 +586,7 @@ theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
 -/
 
 #print FiberBundleCore.localTrivAsLocalEquiv_apply /-
-theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpaceₓ) :
+theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
     (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
@@ -612,7 +612,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
 #print FiberBundleCore.toTopologicalSpace /-
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
 that all the local trivialization are continuous. -/
-instance toTopologicalSpace : TopologicalSpace Z.TotalSpaceₓ :=
+instance toTopologicalSpace : TopologicalSpace Z.TotalSpace :=
   TopologicalSpace.generateFrom <|
     ⋃ (i : ι) (s : Set (B × F)) (s_open : IsOpen s), {(Z i).source ∩ Z i ⁻¹' s}
 #align fiber_bundle_core.to_topological_space FiberBundleCore.toTopologicalSpace
@@ -702,7 +702,7 @@ zero section of a vector bundle. Another example (not yet defined) would be the
 section of the endomorphism bundle of a vector bundle. -/
 theorem continuous_const_section (v : F)
     (h : ∀ i j, ∀ x ∈ Z.baseSet i ∩ Z.baseSet j, Z.coordChange i j x v = v) :
-    Continuous (show B → Z.TotalSpaceₓ from fun x => ⟨x, v⟩) :=
+    Continuous (show B → Z.TotalSpace from fun x => ⟨x, v⟩) :=
   by
   apply continuous_iff_continuousAt.2 fun x => _
   have A : Z.base_set (Z.index_at x) ∈ 𝓝 x :=
@@ -758,7 +758,7 @@ theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
 
 #print FiberBundleCore.localTriv_apply /-
 @[simp, mfld_simps]
-theorem localTriv_apply (p : Z.TotalSpaceₓ) :
+theorem localTriv_apply (p : Z.TotalSpace) :
     (Z.localTriv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_apply
@@ -766,7 +766,7 @@ theorem localTriv_apply (p : Z.TotalSpaceₓ) :
 
 #print FiberBundleCore.localTrivAt_apply /-
 @[simp, mfld_simps]
-theorem localTrivAt_apply (p : Z.TotalSpaceₓ) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
+theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
   rw [local_triv_at, local_triv_apply, coord_change_self]; exact Z.mem_base_set_at p.1
 #align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_apply
 -/
@@ -780,7 +780,7 @@ theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = 
 
 #print FiberBundleCore.mem_localTriv_source /-
 @[simp, mfld_simps]
-theorem mem_localTriv_source (p : Z.TotalSpaceₓ) :
+theorem mem_localTriv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTriv i).source ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_source
@@ -788,17 +788,19 @@ theorem mem_localTriv_source (p : Z.TotalSpaceₓ) :
 
 #print FiberBundleCore.mem_localTrivAt_source /-
 @[simp, mfld_simps]
-theorem mem_localTrivAt_source (p : Z.TotalSpaceₓ) (b : B) :
+theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
     p ∈ (Z.localTrivAt b).source ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_source
 -/
 
-#print FiberBundleCore.mem_source_at /-
+/- warning: fiber_bundle_core.mem_source_at clashes with fiber_bundle_core.mem_local_triv_at_source -> FiberBundleCore.mem_localTrivAt_source
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_localTrivAt_sourceₓ'. -/
+#print FiberBundleCore.mem_localTrivAt_source /-
 @[simp, mfld_simps]
-theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpaceₓ) ∈ (Z.localTrivAt b).source := by
+theorem mem_localTrivAt_source : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
   rw [local_triv_at, mem_local_triv_source]; exact Z.mem_base_set_at b
-#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
+#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_localTrivAt_source
 -/
 
 #print FiberBundleCore.mem_localTriv_target /-
@@ -835,8 +837,7 @@ theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
 #print FiberBundleCore.continuous_totalSpaceMk /-
 /-- The inclusion of a fiber into the total space is a continuous map. -/
 @[continuity]
-theorem continuous_totalSpaceMk (b : B) :
-    Continuous (TotalSpace.mk b : Z.Fiber b → Z.TotalSpaceₓ) :=
+theorem continuous_totalSpaceMk (b : B) : Continuous (TotalSpace.mk b : Z.Fiber b → Z.TotalSpace) :=
   by
   rw [continuous_iff_le_induced, FiberBundleCore.toTopologicalSpace]
   apply le_induced_generateFrom
@@ -868,7 +869,7 @@ theorem continuous_totalSpaceMk (b : B) :
 /-- A fiber bundle constructed from core is indeed a fiber bundle. -/
 instance fiberBundle : FiberBundle F Z.Fiber
     where
-  totalSpaceₓ_mk_inducing b :=
+  totalSpace_mk_inducing b :=
     ⟨by
       refine' le_antisymm _ fun s h => _
       · rw [← continuous_iff_le_induced]
@@ -929,7 +930,7 @@ structure FiberPrebundle where
   continuous_triv_change :
     ∀ (e) (_ : e ∈ pretrivialization_atlas) (e') (_ : e' ∈ pretrivialization_atlas),
       ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
-  totalSpaceₓ_mk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ TotalSpace.mk b)
+  totalSpace_mk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ TotalSpace.mk b)
 #align fiber_prebundle FiberPrebundle
 -/
 
@@ -1071,8 +1072,8 @@ establishes that for the topology constructed on the sigma-type using
 "trivializations" (i.e., homeomorphisms with respect to the constructed topology). -/
 def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
     where
-  totalSpaceₓ_mk_inducing b :=
-    a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpaceₓ_mk_inducing b)
+  totalSpace_mk_inducing b :=
+    a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpace_mk_inducing b)
   trivializationAtlas :=
     {e |
       ∃ (e₀ : _) (he₀ : e₀ ∈ a.pretrivializationAtlas),

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit f7ebde7ee0d1505dfccac8644ae12371aa3c1c9f
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -21,16 +21,14 @@ Mathematically, a (topological) fiber bundle with fiber `F` over a base `B` is a
 point is a direct product.
 
 In our formalism, a fiber bundle is by definition the type
-`bundle.total_space E` where `E : B → Type*` is a function associating to
-`x : B` the fiber over `x`. This type `bundle.total_space E` is just a type synonym for
-`Σ (x : B), E x`, with the interest that one can put another topology than on `Σ (x : B), E x`
-which has the disjoint union topology.
+`bundle.total_space F E` where `E : B → Type*` is a function associating to `x : B` the fiber over
+`x`. This type `bundle.total_space F E` is a type of pairs `(proj : B, snd : E proj)`.
 
-To have a fiber bundle structure on `bundle.total_space E`, one should
+To have a fiber bundle structure on `bundle.total_space F E`, one should
 additionally have the following data:
 
 * `F` should be a topological space;
-* There should be a topology on `bundle.total_space E`, for which the projection to `B` is
+* There should be a topology on `bundle.total_space F E`, for which the projection to `B` is
 a fiber bundle with fiber `F` (in particular, each fiber `E x` is homeomorphic to `F`);
 * For each `x`, the fiber `E x` should be a topological space, and the injection
 from `E x` to `bundle.total_space F E` should be an embedding;
@@ -57,17 +55,16 @@ fiber bundle from trivializations given as local equivalences with minimum addit
 
 ### Construction of a bundle from trivializations
 
-* `bundle.total_space E` is a type synonym for `Σ (x : B), E x`, that we can endow with a suitable
-  topology.
+* `bundle.total_space F E` is the type of pairs `(proj : B, snd : E proj)`. We can use the extra
+  argument `F` to construct topology on the total space.
 * `fiber_bundle_core ι B F` : structure registering how changes of coordinates act
   on the fiber `F` above open subsets of `B`, where local trivializations are indexed by `ι`.
 
 Let `Z : fiber_bundle_core ι B F`. Then we define
 
 * `Z.fiber x`     : the fiber above `x`, homeomorphic to `F` (and defeq to `F` as a type).
-* `Z.total_space` : the total space of `Z`, defined as a `Type` as `Σ (b : B), F`, but with a
-  twisted topology coming from the fiber bundle structure. It is (reducibly) the same as
-  `bundle.total_space Z.fiber`.
+* `Z.total_space` : the total space of `Z`, defined as a `Type*` as `bundle.total_space F Z.fiber`
+                    with a custom topology.
 * `Z.proj`        : projection from `Z.total_space` to `B`. It is continuous.
 * `Z.local_triv i`: for `i : ι`, bundle trivialization above the set `Z.base_set i`, which is an
                     open set in `B`.
@@ -158,8 +155,8 @@ choose for each `x` one specific trivialization around it. We include this choic
 of the `fiber_bundle_core`, as it makes some constructions more
 functorial and it is a nice way to say that the trivializations cover the whole space `B`.
 
-With this definition, the type of the fiber bundle space constructed from the core data is just
-`Σ (b : B), F `, but the topology is not the product one, in general.
+With this definition, the type of the fiber bundle space constructed from the core data is
+`bundle.total_space F (λ b : B, F)`, but the topology is not the product one, in general.
 
 We also take the indexing type (indexing all the trivializations) as a parameter to the fiber bundle
 core: it could always be taken as a subtype of all the maps from open subsets of `B` to continuous
@@ -179,7 +176,7 @@ open TopologicalSpace Filter Set Bundle
 
 open scoped Topology Classical Bundle
 
-attribute [mfld_simps] total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul
+attribute [mfld_simps] total_space.coe_proj total_space.coe_snd coe_snd_map_apply coe_snd_map_smul
   total_space.mk_cast
 
 /-! ### General definition of fiber bundles -/
@@ -188,10 +185,10 @@ attribute [mfld_simps] total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_
 section FiberBundle
 
 variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
-  [TopologicalSpace (TotalSpace E)] [∀ b, TopologicalSpace (E b)]
+  [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpaceₓ_mk_inducing] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
@@ -200,9 +197,9 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/
 class FiberBundle where
-  totalSpaceMk_inducing : ∀ b : B, Inducing (@totalSpaceMk B E b)
-  trivializationAtlas : Set (Trivialization F (π E))
-  trivializationAt : B → Trivialization F (π E)
+  totalSpaceₓ_mk_inducing : ∀ b : B, Inducing (@TotalSpace.mk B F E b)
+  trivializationAtlas : Set (Trivialization F (π F E))
+  trivializationAt : B → Trivialization F (π F E)
   mem_baseSet_trivializationAt : ∀ b : B, b ∈ (trivialization_at b).baseSet
   trivialization_mem_atlas : ∀ b : B, trivialization_at b ∈ trivialization_atlas
 #align fiber_bundle FiberBundle
@@ -219,7 +216,7 @@ bundle.  This is needed because lemmas about the linearity of trivializations or
 functions to `F →L[R] F`, where `F` is the model fiber) of the transition functions are only
 expected to hold for trivializations in the designated atlas. -/
 @[mk_iff]
-class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π E)) : Prop where
+class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π F E)) : Prop where
   out : e ∈ trivializationAtlas F E
 #align mem_trivialization_atlas MemTrivializationAtlas
 -/
@@ -232,7 +229,7 @@ namespace FiberBundle
 variable (F) {E} [FiberBundle F E]
 
 #print FiberBundle.map_proj_nhds /-
-theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
+theorem map_proj_nhds (x : TotalSpace F E) : map (π F E) (𝓝 x) = 𝓝 x.proj :=
   (trivializationAt F E x.proj).map_proj_nhds <|
     (trivializationAt F E x.proj).mem_source.2 <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.map_proj_nhds FiberBundle.map_proj_nhds
@@ -243,14 +240,14 @@ variable (E)
 #print FiberBundle.continuous_proj /-
 /-- The projection from a fiber bundle to its base is continuous. -/
 @[continuity]
-theorem continuous_proj : Continuous (π E) :=
+theorem continuous_proj : Continuous (π F E) :=
   continuous_iff_continuousAt.2 fun x => (map_proj_nhds F x).le
 #align fiber_bundle.continuous_proj FiberBundle.continuous_proj
 -/
 
 #print FiberBundle.isOpenMap_proj /-
 /-- The projection from a fiber bundle to its base is an open map. -/
-theorem isOpenMap_proj : IsOpenMap (π E) :=
+theorem isOpenMap_proj : IsOpenMap (π F E) :=
   IsOpenMap.of_nhds_le fun x => (map_proj_nhds F x).ge
 #align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_proj
 -/
@@ -258,7 +255,7 @@ theorem isOpenMap_proj : IsOpenMap (π E) :=
 #print FiberBundle.surjective_proj /-
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a surjective
 map. -/
-theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
+theorem surjective_proj [Nonempty F] : Function.Surjective (π F E) := fun b =>
   let ⟨p, _, hpb⟩ :=
     (trivializationAt F E b).proj_surjOn_baseSet (mem_baseSet_trivializationAt F E b)
   ⟨p, hpb⟩
@@ -268,14 +265,14 @@ theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
 #print FiberBundle.quotientMap_proj /-
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a quotient
 map. -/
-theorem quotientMap_proj [Nonempty F] : QuotientMap (π E) :=
+theorem quotientMap_proj [Nonempty F] : QuotientMap (π F E) :=
   (isOpenMap_proj F E).to_quotientMap (continuous_proj F E) (surjective_proj F E)
 #align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_proj
 -/
 
 #print FiberBundle.continuous_totalSpaceMk /-
-theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
-  (totalSpaceMk_inducing F E x).Continuous
+theorem continuous_totalSpaceMk (x : B) : Continuous (@TotalSpace.mk B F E x) :=
+  (totalSpace_mk_inducing F E x).Continuous
 #align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMk
 -/
 
@@ -283,7 +280,7 @@ variable {E F}
 
 #print FiberBundle.mem_trivializationAt_proj_source /-
 @[simp, mfld_simps]
-theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
+theorem mem_trivializationAt_proj_source {x : TotalSpace F E} :
     x ∈ (trivializationAt F E x.proj).source :=
   (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
@@ -291,7 +288,7 @@ theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
 
 #print FiberBundle.trivializationAt_proj_fst /-
 @[simp, mfld_simps]
-theorem trivializationAt_proj_fst {x : TotalSpace E} :
+theorem trivializationAt_proj_fst {x : TotalSpace F E} :
     ((trivializationAt F E x.proj) x).1 = x.proj :=
   Trivialization.coe_fst' _ <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.trivialization_at_proj_fst FiberBundle.trivializationAt_proj_fst
@@ -303,7 +300,7 @@ open Trivialization
 
 #print FiberBundle.continuousWithinAt_totalSpace /-
 /-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
-theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
+theorem continuousWithinAt_totalSpace (f : X → TotalSpace F E) {s : Set X} {x₀ : X} :
     ContinuousWithinAt f s x₀ ↔
       ContinuousWithinAt (fun x => (f x).proj) s x₀ ∧
         ContinuousWithinAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) s x₀ :=
@@ -327,7 +324,7 @@ theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀
 
 #print FiberBundle.continuousAt_totalSpace /-
 /-- Characterization of continuous functions (at a point) into a fiber bundle. -/
-theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
+theorem continuousAt_totalSpace (f : X → TotalSpace F E) {x₀ : X} :
     ContinuousAt f x₀ ↔
       ContinuousAt (fun x => (f x).proj) x₀ ∧
         ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ :=
@@ -344,16 +341,16 @@ variable (F E)
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
     [OrderTopology B] [FiberBundle F E] (a b : B) :
-    ∃ e : Trivialization F (π E), Icc a b ⊆ e.baseSet := by
+    ∃ e : Trivialization F (π F E), Icc a b ⊆ e.baseSet := by
   classical
-  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π E), a ∈ ea.baseSet :=
+  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π F E), a ∈ ea.baseSet :=
     ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
   -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
     cases' le_or_lt a b with hab hab <;>
     [skip; exact ⟨ea, by simp [*]⟩]
   /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
     We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
-  set s : Set B := {x ∈ Icc a b | ∃ e : Trivialization F (π E), Icc a x ⊆ e.baseSet}
+  set s : Set B := {x ∈ Icc a b | ∃ e : Trivialization F (π F E), Icc a x ⊆ e.baseSet}
   have ha : a ∈ s := ⟨left_mem_Icc.2 hab, ea, by simp [hea]⟩
   have sne : s.nonempty := ⟨a, ha⟩
   have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
@@ -361,13 +358,13 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   set c := Sup s
   have hsc : IsLUB s c := isLUB_csSup sne sbd
   have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
-  obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
+  obtain ⟨-, ec : Trivialization F (π F E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
     by
     cases' hc.1.eq_or_lt with heq hlt; · rwa [← HEq]
     refine' ⟨hc, _⟩
     /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
         of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
-    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π E), c ∈ ec.baseSet :=
+    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π F E), c ∈ ec.baseSet :=
       ⟨trivialization_at F E c, mem_base_set_trivialization_at F E c⟩
     obtain ⟨c', hc', hc'e⟩ : ∃ c' ∈ Ico a c, Ioc c' c ⊆ ec.base_set :=
       (mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset hlt).1
@@ -382,7 +379,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
   cases' hc.2.eq_or_lt with heq hlt
   · exact ⟨ec, HEq ▸ hec⟩
-  rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π E), Icc a d ⊆ e.baseSet
+  rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
   · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
   /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
     `d ∈ (c, b]`. -/
@@ -394,7 +391,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   · /- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
         Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
         a trivialization over `[a, d]`. -/
-    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π E), d ∈ ed.baseSet :=
+    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π F E), d ∈ ed.baseSet :=
       ⟨trivialization_at F E d, mem_base_set_trivialization_at F E d⟩
     refine'
       ⟨d, hdcb,
@@ -473,31 +470,25 @@ def Fiber (x : B) :=
 #align fiber_bundle_core.fiber FiberBundleCore.Fiber
 -/
 
-section FiberInstances
-
-attribute [local reducible] fiber
-
 #print FiberBundleCore.topologicalSpaceFiber /-
-instance topologicalSpaceFiber (x : B) : TopologicalSpace (Z.Fiber x) := by infer_instance
+instance topologicalSpaceFiber (x : B) : TopologicalSpace (Z.Fiber x) :=
+  ‹TopologicalSpace F›
 #align fiber_bundle_core.topological_space_fiber FiberBundleCore.topologicalSpaceFiber
 -/
 
-end FiberInstances
-
 #print FiberBundleCore.TotalSpace /-
 /-- The total space of the fiber bundle, as a convenience function for dot notation.
-It is by definition equal to `bundle.total_space Z.fiber`, a.k.a. `Σ x, Z.fiber x` but with a
-different name for typeclass inference. -/
+It is by definition equal to `bundle.total_space Z.fiber` -/
 @[nolint unused_arguments, reducible]
 def TotalSpace :=
-  Bundle.TotalSpace Z.Fiber
+  Bundle.TotalSpace F Z.Fiber
 #align fiber_bundle_core.total_space FiberBundleCore.TotalSpace
 -/
 
 #print FiberBundleCore.proj /-
 /-- The projection from the total space of a fiber bundle core, on its base. -/
 @[reducible, simp, mfld_simps]
-def proj : Z.TotalSpace → B :=
+def proj : Z.TotalSpaceₓ → B :=
   Bundle.TotalSpace.proj
 #align fiber_bundle_core.proj FiberBundleCore.proj
 -/
@@ -552,7 +543,7 @@ The local trivialization will ultimately be a local homeomorphism. For now, we o
 local equiv version, denoted with a prime. In further developments, avoid this auxiliary version,
 and use `Z.local_triv` instead.
 -/
-def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
+def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpaceₓ (B × F)
     where
   source := Z.proj ⁻¹' Z.baseSet i
   target := Z.baseSet i ×ˢ univ
@@ -581,7 +572,7 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
 variable (i : ι)
 
 #print FiberBundleCore.mem_localTrivAsLocalEquiv_source /-
-theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
+theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpaceₓ) :
     p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
@@ -595,7 +586,7 @@ theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
 -/
 
 #print FiberBundleCore.localTrivAsLocalEquiv_apply /-
-theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
+theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpaceₓ) :
     (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
@@ -621,7 +612,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
 #print FiberBundleCore.toTopologicalSpace /-
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
 that all the local trivialization are continuous. -/
-instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace Z.Fiber) :=
+instance toTopologicalSpace : TopologicalSpace Z.TotalSpaceₓ :=
   TopologicalSpace.generateFrom <|
     ⋃ (i : ι) (s : Set (B × F)) (s_open : IsOpen s), {(Z i).source ∩ Z i ⁻¹' s}
 #align fiber_bundle_core.to_topological_space FiberBundleCore.toTopologicalSpace
@@ -692,7 +683,7 @@ def localTriv (i : ι) : Trivialization F Z.proj
 #print FiberBundleCore.localTrivAt /-
 /-- Preferred local trivialization of a fiber bundle constructed from core, at a given point, as
 a bundle trivialization -/
-def localTrivAt (b : B) : Trivialization F (π Z.Fiber) :=
+def localTrivAt (b : B) : Trivialization F (π F Z.Fiber) :=
   Z.localTriv (Z.indexAt b)
 #align fiber_bundle_core.local_triv_at FiberBundleCore.localTrivAt
 -/
@@ -711,7 +702,7 @@ zero section of a vector bundle. Another example (not yet defined) would be the
 section of the endomorphism bundle of a vector bundle. -/
 theorem continuous_const_section (v : F)
     (h : ∀ i j, ∀ x ∈ Z.baseSet i ∩ Z.baseSet j, Z.coordChange i j x v = v) :
-    Continuous (show B → Z.TotalSpace from fun x => ⟨x, v⟩) :=
+    Continuous (show B → Z.TotalSpaceₓ from fun x => ⟨x, v⟩) :=
   by
   apply continuous_iff_continuousAt.2 fun x => _
   have A : Z.base_set (Z.index_at x) ∈ 𝓝 x :=
@@ -767,7 +758,7 @@ theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
 
 #print FiberBundleCore.localTriv_apply /-
 @[simp, mfld_simps]
-theorem localTriv_apply (p : Z.TotalSpace) :
+theorem localTriv_apply (p : Z.TotalSpaceₓ) :
     (Z.localTriv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_apply
@@ -775,7 +766,7 @@ theorem localTriv_apply (p : Z.TotalSpace) :
 
 #print FiberBundleCore.localTrivAt_apply /-
 @[simp, mfld_simps]
-theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
+theorem localTrivAt_apply (p : Z.TotalSpaceₓ) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
   rw [local_triv_at, local_triv_apply, coord_change_self]; exact Z.mem_base_set_at p.1
 #align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_apply
 -/
@@ -789,7 +780,7 @@ theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = 
 
 #print FiberBundleCore.mem_localTriv_source /-
 @[simp, mfld_simps]
-theorem mem_localTriv_source (p : Z.TotalSpace) :
+theorem mem_localTriv_source (p : Z.TotalSpaceₓ) :
     p ∈ (Z.localTriv i).source ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_source
@@ -797,7 +788,7 @@ theorem mem_localTriv_source (p : Z.TotalSpace) :
 
 #print FiberBundleCore.mem_localTrivAt_source /-
 @[simp, mfld_simps]
-theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
+theorem mem_localTrivAt_source (p : Z.TotalSpaceₓ) (b : B) :
     p ∈ (Z.localTrivAt b).source ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_source
@@ -805,7 +796,7 @@ theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
 
 #print FiberBundleCore.mem_source_at /-
 @[simp, mfld_simps]
-theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
+theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpaceₓ) ∈ (Z.localTrivAt b).source := by
   rw [local_triv_at, mem_local_triv_source]; exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
 -/
@@ -845,11 +836,11 @@ theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
 /-- The inclusion of a fiber into the total space is a continuous map. -/
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
-    Continuous (totalSpaceMk b : Z.Fiber b → Bundle.TotalSpace Z.Fiber) :=
+    Continuous (TotalSpace.mk b : Z.Fiber b → Z.TotalSpaceₓ) :=
   by
   rw [continuous_iff_le_induced, FiberBundleCore.toTopologicalSpace]
   apply le_induced_generateFrom
-  simp only [total_space_mk, mem_Union, mem_singleton_iff, local_triv_as_local_equiv_source,
+  simp only [mem_Union, mem_singleton_iff, local_triv_as_local_equiv_source,
     local_triv_as_local_equiv_coe]
   rintro s ⟨i, t, ht, rfl⟩
   rw [← (Z.local_triv i).source_inter_preimage_target_inter t, preimage_inter, ← preimage_comp,
@@ -877,7 +868,7 @@ theorem continuous_totalSpaceMk (b : B) :
 /-- A fiber bundle constructed from core is indeed a fiber bundle. -/
 instance fiberBundle : FiberBundle F Z.Fiber
     where
-  totalSpaceMk_inducing b :=
+  totalSpaceₓ_mk_inducing b :=
     ⟨by
       refine' le_antisymm _ fun s h => _
       · rw [← continuous_iff_le_induced]
@@ -889,7 +880,6 @@ instance fiberBundle : FiberBundle F Z.Fiber
                 (Z.local_triv_at b).continuous_toFun _ ((Z.local_triv_at b).open_baseSet.Prod h),
               _⟩
         rw [preimage_inter, ← preimage_comp, Function.comp]
-        simp only [total_space_mk]
         refine' ext_iff.mpr fun a => ⟨fun ha => _, fun ha => ⟨Z.mem_base_set_at b, _⟩⟩
         · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk] at ha 
           exact ha.2.2
@@ -932,25 +922,25 @@ topology in such a way that there is a fiber bundle structure for which the loca
 are also local homeomorphism and hence local trivializations. -/
 @[nolint has_nonempty_instance]
 structure FiberPrebundle where
-  pretrivializationAtlas : Set (Pretrivialization F (π E))
-  pretrivializationAt : B → Pretrivialization F (π E)
+  pretrivializationAtlas : Set (Pretrivialization F (π F E))
+  pretrivializationAt : B → Pretrivialization F (π F E)
   mem_base_pretrivializationAt : ∀ x : B, x ∈ (pretrivialization_at x).baseSet
   pretrivialization_mem_atlas : ∀ x : B, pretrivialization_at x ∈ pretrivialization_atlas
   continuous_triv_change :
     ∀ (e) (_ : e ∈ pretrivialization_atlas) (e') (_ : e' ∈ pretrivialization_atlas),
       ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
-  totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ totalSpaceMk b)
+  totalSpaceₓ_mk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ TotalSpace.mk b)
 #align fiber_prebundle FiberPrebundle
 -/
 
 namespace FiberPrebundle
 
-variable {F E} (a : FiberPrebundle F E) {e : Pretrivialization F (π E)}
+variable {F E} (a : FiberPrebundle F E) {e : Pretrivialization F (π F E)}
 
 #print FiberPrebundle.totalSpaceTopology /-
 /-- Topology on the total space that will make the prebundle into a bundle. -/
-def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E) :=
-  ⨆ (e : Pretrivialization F (π E)) (he : e ∈ a.pretrivializationAtlas),
+def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace F E) :=
+  ⨆ (e : Pretrivialization F (π F E)) (he : e ∈ a.pretrivializationAtlas),
     coinduced e.setSymm Subtype.topologicalSpace
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
 -/
@@ -967,7 +957,7 @@ theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializ
 -/
 
 #print FiberPrebundle.isOpen_source /-
-theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTopology] e.source :=
+theorem isOpen_source (e : Pretrivialization F (π F E)) : is_open[a.totalSpaceTopology] e.source :=
   by
   letI := a.total_space_topology
   refine' is_open_supr_iff.mpr fun e' => _
@@ -980,7 +970,7 @@ theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTop
 -/
 
 #print FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter /-
-theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π E))
+theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π F E))
     (he' : e' ∈ a.pretrivializationAtlas) :
     IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) :=
   by
@@ -996,7 +986,7 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
 #print FiberPrebundle.trivializationOfMemPretrivializationAtlas /-
 /-- Promotion from a `pretrivialization` to a `trivialization`. -/
 def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
-    @Trivialization B F _ _ _ a.totalSpaceTopology (π E) :=
+    @Trivialization B F _ _ _ a.totalSpaceTopology (π F E) :=
   { e with
     open_source := a.isOpen_source e
     continuous_toFun := by
@@ -1021,7 +1011,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
 
 #print FiberPrebundle.mem_pretrivializationAt_source /-
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
-    totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
+    TotalSpace.mk b x ∈ (a.pretrivializationAt b).source :=
   by
   simp only [(a.pretrivialization_at b).source_eq, mem_preimage, total_space.proj]
   exact a.mem_base_pretrivialization_at b
@@ -1031,7 +1021,7 @@ theorem mem_pretrivializationAt_source (b : B) (x : E b) :
 #print FiberPrebundle.totalSpaceMk_preimage_source /-
 @[simp]
 theorem totalSpaceMk_preimage_source (b : B) :
-    totalSpaceMk b ⁻¹' (a.pretrivializationAt b).source = univ :=
+    TotalSpace.mk b ⁻¹' (a.pretrivializationAt b).source = univ :=
   by
   apply eq_univ_of_univ_subset
   rw [(a.pretrivialization_at b).source_eq, ← preimage_comp, Function.comp]
@@ -1043,7 +1033,8 @@ theorem totalSpaceMk_preimage_source (b : B) :
 
 #print FiberPrebundle.continuous_totalSpaceMk /-
 @[continuity]
-theorem continuous_totalSpaceMk (b : B) : @Continuous _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
+theorem continuous_totalSpaceMk (b : B) :
+    @Continuous _ _ _ a.totalSpaceTopology (TotalSpace.mk b) :=
   by
   letI := a.total_space_topology
   let e := a.trivialization_of_mem_pretrivialization_atlas (a.pretrivialization_mem_atlas b)
@@ -1055,8 +1046,8 @@ theorem continuous_totalSpaceMk (b : B) : @Continuous _ _ _ a.totalSpaceTopology
 
 #print FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp /-
 theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
-    (h : Inducing (a.pretrivializationAt b ∘ totalSpaceMk b)) :
-    @Inducing _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
+    (h : Inducing (a.pretrivializationAt b ∘ TotalSpace.mk b)) :
+    @Inducing _ _ _ a.totalSpaceTopology (TotalSpace.mk b) :=
   by
   letI := a.total_space_topology
   rw [← restrict_comp_cod_restrict (a.mem_trivialization_at_source b)] at h 
@@ -1080,7 +1071,8 @@ establishes that for the topology constructed on the sigma-type using
 "trivializations" (i.e., homeomorphisms with respect to the constructed topology). -/
 def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
     where
-  totalSpaceMk_inducing b := a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpaceMk_inducing b)
+  totalSpaceₓ_mk_inducing b :=
+    a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpaceₓ_mk_inducing b)
   trivializationAtlas :=
     {e |
       ∃ (e₀ : _) (he₀ : e₀ ∈ a.pretrivializationAtlas),
@@ -1093,7 +1085,7 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
 -/
 
 #print FiberPrebundle.continuous_proj /-
-theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
+theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π F E) :=
   by
   letI := a.total_space_topology
   letI := a.to_fiber_bundle
@@ -1104,19 +1096,19 @@ theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print FiberPrebundle.continuousOn_of_comp_right /-
 /-- For a fiber bundle `E` over `B` constructed using the `fiber_prebundle` mechanism,
-continuity of a function `total_space E → X` on an open set `s` can be checked by precomposing at
+continuity of a function `total_space F E → X` on an open set `s` can be checked by precomposing at
 each point with the pretrivialization used for the construction at that point. -/
-theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalSpace E → X}
+theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalSpace F E → X}
     {s : Set B} (hs : IsOpen s)
     (hf :
       ∀ b ∈ s,
         ContinuousOn (f ∘ (a.pretrivializationAt b).toLocalEquiv.symm)
           ((s ∩ (a.pretrivializationAt b).baseSet) ×ˢ (Set.univ : Set F))) :
-    @ContinuousOn _ _ a.totalSpaceTopology _ f (π E ⁻¹' s) :=
+    @ContinuousOn _ _ a.totalSpaceTopology _ f (π F E ⁻¹' s) :=
   by
   letI := a.total_space_topology
   intro z hz
-  let e : Trivialization F (π E) :=
+  let e : Trivialization F (π F E) :=
     a.trivialization_of_mem_pretrivialization_atlas (a.pretrivialization_mem_atlas z.proj)
   refine'
     (e.continuous_at_of_comp_right _

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

@@ -191,11 +191,11 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/
@@ -231,24 +231,31 @@ namespace FiberBundle
 
 variable (F) {E} [FiberBundle F E]
 
+#print FiberBundle.map_proj_nhds /-
 theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
   (trivializationAt F E x.proj).map_proj_nhds <|
     (trivializationAt F E x.proj).mem_source.2 <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.map_proj_nhds FiberBundle.map_proj_nhds
+-/
 
 variable (E)
 
+#print FiberBundle.continuous_proj /-
 /-- The projection from a fiber bundle to its base is continuous. -/
 @[continuity]
 theorem continuous_proj : Continuous (π E) :=
   continuous_iff_continuousAt.2 fun x => (map_proj_nhds F x).le
 #align fiber_bundle.continuous_proj FiberBundle.continuous_proj
+-/
 
+#print FiberBundle.isOpenMap_proj /-
 /-- The projection from a fiber bundle to its base is an open map. -/
 theorem isOpenMap_proj : IsOpenMap (π E) :=
   IsOpenMap.of_nhds_le fun x => (map_proj_nhds F x).ge
 #align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_proj
+-/
 
+#print FiberBundle.surjective_proj /-
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a surjective
 map. -/
 theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
@@ -256,35 +263,45 @@ theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
     (trivializationAt F E b).proj_surjOn_baseSet (mem_baseSet_trivializationAt F E b)
   ⟨p, hpb⟩
 #align fiber_bundle.surjective_proj FiberBundle.surjective_proj
+-/
 
+#print FiberBundle.quotientMap_proj /-
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a quotient
 map. -/
 theorem quotientMap_proj [Nonempty F] : QuotientMap (π E) :=
   (isOpenMap_proj F E).to_quotientMap (continuous_proj F E) (surjective_proj F E)
 #align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_proj
+-/
 
+#print FiberBundle.continuous_totalSpaceMk /-
 theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
   (totalSpaceMk_inducing F E x).Continuous
 #align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMk
+-/
 
 variable {E F}
 
+#print FiberBundle.mem_trivializationAt_proj_source /-
 @[simp, mfld_simps]
 theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
     x ∈ (trivializationAt F E x.proj).source :=
   (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
+-/
 
+#print FiberBundle.trivializationAt_proj_fst /-
 @[simp, mfld_simps]
 theorem trivializationAt_proj_fst {x : TotalSpace E} :
     ((trivializationAt F E x.proj) x).1 = x.proj :=
   Trivialization.coe_fst' _ <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.trivialization_at_proj_fst FiberBundle.trivializationAt_proj_fst
+-/
 
 variable (F)
 
 open Trivialization
 
+#print FiberBundle.continuousWithinAt_totalSpace /-
 /-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
 theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
     ContinuousWithinAt f s x₀ ↔
@@ -306,7 +323,9 @@ theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀
   · apply mem_trivialization_at_proj_source
   · rwa [source_eq, preimage_preimage]
 #align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
+-/
 
+#print FiberBundle.continuousAt_totalSpace /-
 /-- Characterization of continuous functions (at a point) into a fiber bundle. -/
 theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
     ContinuousAt f x₀ ↔
@@ -314,11 +333,13 @@ theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
         ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ :=
   by simp_rw [← continuousWithinAt_univ]; exact continuous_within_at_total_space F f
 #align fiber_bundle.continuous_at_total_space FiberBundle.continuousAt_totalSpace
+-/
 
 end FiberBundle
 
 variable (F E)
 
+#print FiberBundle.exists_trivialization_Icc_subset /-
 /-- If `E` is a fiber bundle over a conditionally complete linear order,
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
@@ -387,6 +408,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     rw [disjoint_left] at he ; push_neg at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
     exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
+-/
 
 end FiberBundle
 
@@ -426,8 +448,6 @@ namespace FiberBundleCore
 
 variable [TopologicalSpace B] [TopologicalSpace F] (Z : FiberBundleCore ι B F)
 
-include Z
-
 #print FiberBundleCore.Index /-
 /-- The index set of a fiber bundle core, as a convenience function for dot notation -/
 @[nolint unused_arguments has_nonempty_instance]
@@ -484,6 +504,7 @@ def proj : Z.TotalSpace → B :=
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberBundleCore.trivChange /-
 /-- Local homeomorphism version of the trivialization change. -/
 def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
     where
@@ -512,11 +533,14 @@ def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
     simpa [inter_comm] using
       ContinuousOn.prod continuous_fst.continuous_on (Z.continuous_on_coord_change j i)
 #align fiber_bundle_core.triv_change FiberBundleCore.trivChange
+-/
 
+#print FiberBundleCore.mem_trivChange_source /-
 @[simp, mfld_simps]
 theorem mem_trivChange_source (i j : ι) (p : B × F) :
     p ∈ (Z.trivChange i j).source ↔ p.1 ∈ Z.baseSet i ∩ Z.baseSet j := by erw [mem_prod]; simp
 #align fiber_bundle_core.mem_triv_change_source FiberBundleCore.mem_trivChange_source
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print FiberBundleCore.localTrivAsLocalEquiv /-
@@ -556,21 +580,28 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
 
 variable (i : ι)
 
+#print FiberBundleCore.mem_localTrivAsLocalEquiv_source /-
 theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
+-/
 
+#print FiberBundleCore.mem_localTrivAsLocalEquiv_target /-
 theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
     p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i := by erw [mem_prod];
   simp only [and_true_iff, mem_univ]
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_target
+-/
 
+#print FiberBundleCore.localTrivAsLocalEquiv_apply /-
 theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
     (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
+-/
 
+#print FiberBundleCore.localTrivAsLocalEquiv_trans /-
 /-- The composition of two local trivializations is the trivialization change Z.triv_change i j. -/
 theorem localTrivAsLocalEquiv_trans (i j : ι) :
     (Z.localTrivAsLocalEquiv i).symm.trans (Z.localTrivAsLocalEquiv j) ≈
@@ -585,6 +616,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
       LocalEquiv.coe_trans, total_space.proj] at hx ⊢
     simp only [Z.coord_change_comp, hx, mem_inter_iff, and_self_iff, mem_base_set_at]
 #align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_trans
+-/
 
 #print FiberBundleCore.toTopologicalSpace /-
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
@@ -598,6 +630,7 @@ instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace Z.Fiber) :=
 variable (b : B) (a : F)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberBundleCore.open_source' /-
 theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
   by
   apply TopologicalSpace.GenerateOpen.basic
@@ -607,6 +640,7 @@ theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
   simp only [local_triv_as_local_equiv_apply, prod_mk_mem_set_prod_eq, mem_inter_iff, and_self_iff,
     mem_local_triv_as_local_equiv_source, and_true_iff, mem_univ, mem_preimage]
 #align fiber_bundle_core.open_source' FiberBundleCore.open_source'
+-/
 
 #print FiberBundleCore.localTriv /-
 /-- Extended version of the local trivialization of a fiber bundle constructed from core,
@@ -663,11 +697,14 @@ def localTrivAt (b : B) : Trivialization F (π Z.Fiber) :=
 #align fiber_bundle_core.local_triv_at FiberBundleCore.localTrivAt
 -/
 
+#print FiberBundleCore.localTrivAt_def /-
 @[simp, mfld_simps]
 theorem localTrivAt_def (b : B) : Z.localTriv (Z.indexAt b) = Z.localTrivAt b :=
   rfl
 #align fiber_bundle_core.local_triv_at_def FiberBundleCore.localTrivAt_def
+-/
 
+#print FiberBundleCore.continuous_const_section /-
 /-- If an element of `F` is invariant under all coordinate changes, then one can define a
 corresponding section of the fiber bundle, which is continuous. This applies in particular to the
 zero section of a vector bundle. Another example (not yet defined) would be the identity
@@ -688,90 +725,121 @@ theorem continuous_const_section (v : F)
     simp only [h, hy, mem_base_set_at, mfld_simps]
   · exact A
 #align fiber_bundle_core.continuous_const_section FiberBundleCore.continuous_const_section
+-/
 
+#print FiberBundleCore.localTrivAsLocalEquiv_coe /-
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv i :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsLocalEquiv_coe
+-/
 
+#print FiberBundleCore.localTrivAsLocalEquiv_source /-
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_source :
     (Z.localTrivAsLocalEquiv i).source = (Z.localTriv i).source :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsLocalEquiv_source
+-/
 
+#print FiberBundleCore.localTrivAsLocalEquiv_target /-
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_target :
     (Z.localTrivAsLocalEquiv i).target = (Z.localTriv i).target :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsLocalEquiv_target
+-/
 
+#print FiberBundleCore.localTrivAsLocalEquiv_symm /-
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_symm :
     (Z.localTrivAsLocalEquiv i).symm = (Z.localTriv i).toLocalEquiv.symm :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsLocalEquiv_symm
+-/
 
+#print FiberBundleCore.baseSet_at /-
 @[simp, mfld_simps]
 theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
   rfl
 #align fiber_bundle_core.base_set_at FiberBundleCore.baseSet_at
+-/
 
+#print FiberBundleCore.localTriv_apply /-
 @[simp, mfld_simps]
 theorem localTriv_apply (p : Z.TotalSpace) :
     (Z.localTriv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_apply
+-/
 
+#print FiberBundleCore.localTrivAt_apply /-
 @[simp, mfld_simps]
 theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
   rw [local_triv_at, local_triv_apply, coord_change_self]; exact Z.mem_base_set_at p.1
 #align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_apply
+-/
 
+#print FiberBundleCore.localTrivAt_apply_mk /-
 @[simp, mfld_simps]
 theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = ⟨b, a⟩ :=
   Z.localTrivAt_apply _
 #align fiber_bundle_core.local_triv_at_apply_mk FiberBundleCore.localTrivAt_apply_mk
+-/
 
+#print FiberBundleCore.mem_localTriv_source /-
 @[simp, mfld_simps]
 theorem mem_localTriv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTriv i).source ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_source
+-/
 
+#print FiberBundleCore.mem_localTrivAt_source /-
 @[simp, mfld_simps]
 theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
     p ∈ (Z.localTrivAt b).source ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_source
+-/
 
+#print FiberBundleCore.mem_source_at /-
 @[simp, mfld_simps]
 theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
   rw [local_triv_at, mem_local_triv_source]; exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
+-/
 
+#print FiberBundleCore.mem_localTriv_target /-
 @[simp, mfld_simps]
 theorem mem_localTriv_target (p : B × F) :
     p ∈ (Z.localTriv i).target ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Trivialization.mem_target _
 #align fiber_bundle_core.mem_local_triv_target FiberBundleCore.mem_localTriv_target
+-/
 
+#print FiberBundleCore.mem_localTrivAt_target /-
 @[simp, mfld_simps]
 theorem mem_localTrivAt_target (p : B × F) (b : B) :
     p ∈ (Z.localTrivAt b).target ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Trivialization.mem_target _
 #align fiber_bundle_core.mem_local_triv_at_target FiberBundleCore.mem_localTrivAt_target
+-/
 
+#print FiberBundleCore.localTriv_symm_apply /-
 @[simp, mfld_simps]
 theorem localTriv_symm_apply (p : B × F) :
     (Z.localTriv i).toLocalHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_apply
+-/
 
+#print FiberBundleCore.mem_localTrivAt_baseSet /-
 @[simp, mfld_simps]
 theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
   rw [local_triv_at, ← base_set_at]; exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSet
+-/
 
 #print FiberBundleCore.continuous_totalSpaceMk /-
 /-- The inclusion of a fiber into the total space is a continuous map. -/
@@ -834,15 +902,19 @@ instance fiberBundle : FiberBundle F Z.Fiber
 #align fiber_bundle_core.fiber_bundle FiberBundleCore.fiberBundle
 -/
 
+#print FiberBundleCore.continuous_proj /-
 /-- The projection on the base of a fiber bundle created from core is continuous -/
 theorem continuous_proj : Continuous Z.proj :=
   continuous_proj F Z.Fiber
 #align fiber_bundle_core.continuous_proj FiberBundleCore.continuous_proj
+-/
 
+#print FiberBundleCore.isOpenMap_proj /-
 /-- The projection on the base of a fiber bundle created from core is an open map -/
 theorem isOpenMap_proj : IsOpenMap Z.proj :=
   isOpenMap_proj F Z.Fiber
 #align fiber_bundle_core.is_open_map_proj FiberBundleCore.isOpenMap_proj
+-/
 
 end FiberBundleCore
 
@@ -883,6 +955,7 @@ def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
 -/
 
+#print FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas /-
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
   by
@@ -891,7 +964,9 @@ theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializ
       id fun U h => preimage_nhdsWithin_coinduced' H e.open_target (le_def.1 (nhds_mono _) U h)
   exact le_iSup₂ e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
+-/
 
+#print FiberPrebundle.isOpen_source /-
 theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTopology] e.source :=
   by
   letI := a.total_space_topology
@@ -902,7 +977,9 @@ theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTop
     Subtype.preimage_coe_eq_preimage_coe_iff, e'.target_eq, prod_inter_prod, inter_univ,
     Pretrivialization.preimage_symm_proj_inter]
 #align fiber_prebundle.is_open_source FiberPrebundle.isOpen_source
+-/
 
+#print FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter /-
 theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π E))
     (he' : e' ∈ a.pretrivializationAtlas) :
     IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) :=
@@ -914,6 +991,7 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
   rw [inter_comm, hu2]
   exact hu1.inter e'.open_target
 #align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter
+-/
 
 #print FiberPrebundle.trivializationOfMemPretrivializationAtlas /-
 /-- Promotion from a `pretrivialization` to a `trivialization`. -/
@@ -941,13 +1019,16 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
 -/
 
+#print FiberPrebundle.mem_pretrivializationAt_source /-
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
     totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
   by
   simp only [(a.pretrivialization_at b).source_eq, mem_preimage, total_space.proj]
   exact a.mem_base_pretrivialization_at b
 #align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_pretrivializationAt_source
+-/
 
+#print FiberPrebundle.totalSpaceMk_preimage_source /-
 @[simp]
 theorem totalSpaceMk_preimage_source (b : B) :
     totalSpaceMk b ⁻¹' (a.pretrivializationAt b).source = univ :=
@@ -958,7 +1039,9 @@ theorem totalSpaceMk_preimage_source (b : B) :
   rw [preimage_const_of_mem _]
   exact a.mem_base_pretrivialization_at b
 #align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_source
+-/
 
+#print FiberPrebundle.continuous_totalSpaceMk /-
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) : @Continuous _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
   by
@@ -968,7 +1051,9 @@ theorem continuous_totalSpaceMk (b : B) : @Continuous _ _ _ a.totalSpaceTopology
       (a.total_space_mk_preimage_source b)]
   exact continuous_iff_le_induced.mpr (le_antisymm_iff.mp (a.total_space_mk_inducing b).induced).1
 #align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMk
+-/
 
+#print FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp /-
 theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
     (h : Inducing (a.pretrivializationAt b ∘ totalSpaceMk b)) :
     @Inducing _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
@@ -984,6 +1069,7 @@ theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
       h
   exact (a.continuous_total_space_mk b).codRestrict (a.mem_trivialization_at_source b)
 #align fiber_prebundle.inducing_total_space_mk_of_inducing_comp FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp
+-/
 
 #print FiberPrebundle.toFiberBundle /-
 /-- Make a `fiber_bundle` from a `fiber_prebundle`.  Concretely this means
@@ -1006,14 +1092,17 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
 #align fiber_prebundle.to_fiber_bundle FiberPrebundle.toFiberBundle
 -/
 
+#print FiberPrebundle.continuous_proj /-
 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   by
   letI := a.total_space_topology
   letI := a.to_fiber_bundle
   exact continuous_proj F E
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberPrebundle.continuousOn_of_comp_right /-
 /-- For a fiber bundle `E` over `B` constructed using the `fiber_prebundle` mechanism,
 continuity of a function `total_space E → X` on an open set `s` can be checked by precomposing at
 each point with the pretrivialization used for the construction at that point. -/
@@ -1040,6 +1129,7 @@ theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalS
   · rw [e.mem_source]
     exact a.mem_base_pretrivialization_at z.proj
 #align fiber_prebundle.continuous_on_of_comp_right FiberPrebundle.continuousOn_of_comp_right
+-/
 
 end FiberPrebundle
 

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

@@ -853,7 +853,7 @@ variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
   [∀ x, TopologicalSpace (E x)]
 
 #print FiberPrebundle /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the local equivalences

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

@@ -191,11 +191,11 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/
@@ -325,68 +325,67 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     [OrderTopology B] [FiberBundle F E] (a b : B) :
     ∃ e : Trivialization F (π E), Icc a b ⊆ e.baseSet := by
   classical
-    obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π E), a ∈ ea.baseSet :=
-      ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
-    -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
-      cases' le_or_lt a b with hab hab <;>
-      [skip; exact ⟨ea, by simp [*]⟩]
-    /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
-      We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
-    set s : Set B := { x ∈ Icc a b | ∃ e : Trivialization F (π E), Icc a x ⊆ e.baseSet }
-    have ha : a ∈ s := ⟨left_mem_Icc.2 hab, ea, by simp [hea]⟩
-    have sne : s.nonempty := ⟨a, ha⟩
-    have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
-    have sbd : BddAbove s := ⟨b, hsb⟩
-    set c := Sup s
-    have hsc : IsLUB s c := isLUB_csSup sne sbd
-    have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
-    obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
-      by
-      cases' hc.1.eq_or_lt with heq hlt; · rwa [← HEq]
-      refine' ⟨hc, _⟩
-      /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
-          of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
-      obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π E), c ∈ ec.baseSet :=
-        ⟨trivialization_at F E c, mem_base_set_trivialization_at F E c⟩
-      obtain ⟨c', hc', hc'e⟩ : ∃ c' ∈ Ico a c, Ioc c' c ⊆ ec.base_set :=
-        (mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset hlt).1
-          (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set hc)
-      /- Since `c' < c = Sup s`, there exists `d ∈ s ∩ (c', c]`. Let `ead` be a trivialization of
-          `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
-      obtain ⟨d, ⟨hdab, ead, had⟩, hd⟩ : ∃ d ∈ s, d ∈ Ioc c' c := hsc.exists_between hc'.2
-      refine' ⟨ead.piecewise_le ec d (had ⟨hdab.1, le_rfl⟩) (hc'e hd), subset_ite.2 _⟩
-      refine'
-        ⟨fun x hx => had ⟨hx.1.1, hx.2⟩, fun x hx => hc'e ⟨hd.1.trans (not_le.1 hx.2), hx.1.2⟩⟩
-    /- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
-      done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
-      `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
-    cases' hc.2.eq_or_lt with heq hlt
-    · exact ⟨ec, HEq ▸ hec⟩
-    rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π E), Icc a d ⊆ e.baseSet
-    · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
-    /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
-      `d ∈ (c, b]`. -/
-    obtain ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, Ico c d ⊆ ec.base_set :=
-      (mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset hlt).1
-        (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set (hec ⟨hc.1, le_rfl⟩))
-    have had : Ico a d ⊆ ec.base_set := Ico_subset_Icc_union_Ico.trans (union_subset hec hd)
-    by_cases he : Disjoint (Iio d) (Ioi c)
-    · /- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
-          Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
-          a trivialization over `[a, d]`. -/
-      obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π E), d ∈ ed.baseSet :=
-        ⟨trivialization_at F E d, mem_base_set_trivialization_at F E d⟩
-      refine'
-        ⟨d, hdcb,
-          (ec.restr_open (Iio d) isOpen_Iio).disjointUnion (ed.restr_open (Ioi c) isOpen_Ioi)
-            (he.mono (inter_subset_right _ _) (inter_subset_right _ _)),
-          fun x hx => _⟩
-      rcases hx.2.eq_or_lt with (rfl | hxd)
-      exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
-    · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
-          `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
-      rw [disjoint_left] at he ; push_neg  at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
-      exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
+  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π E), a ∈ ea.baseSet :=
+    ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
+  -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
+    cases' le_or_lt a b with hab hab <;>
+    [skip; exact ⟨ea, by simp [*]⟩]
+  /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
+    We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
+  set s : Set B := {x ∈ Icc a b | ∃ e : Trivialization F (π E), Icc a x ⊆ e.baseSet}
+  have ha : a ∈ s := ⟨left_mem_Icc.2 hab, ea, by simp [hea]⟩
+  have sne : s.nonempty := ⟨a, ha⟩
+  have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
+  have sbd : BddAbove s := ⟨b, hsb⟩
+  set c := Sup s
+  have hsc : IsLUB s c := isLUB_csSup sne sbd
+  have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
+  obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
+    by
+    cases' hc.1.eq_or_lt with heq hlt; · rwa [← HEq]
+    refine' ⟨hc, _⟩
+    /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
+        of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
+    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π E), c ∈ ec.baseSet :=
+      ⟨trivialization_at F E c, mem_base_set_trivialization_at F E c⟩
+    obtain ⟨c', hc', hc'e⟩ : ∃ c' ∈ Ico a c, Ioc c' c ⊆ ec.base_set :=
+      (mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset hlt).1
+        (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set hc)
+    /- Since `c' < c = Sup s`, there exists `d ∈ s ∩ (c', c]`. Let `ead` be a trivialization of
+        `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
+    obtain ⟨d, ⟨hdab, ead, had⟩, hd⟩ : ∃ d ∈ s, d ∈ Ioc c' c := hsc.exists_between hc'.2
+    refine' ⟨ead.piecewise_le ec d (had ⟨hdab.1, le_rfl⟩) (hc'e hd), subset_ite.2 _⟩
+    refine' ⟨fun x hx => had ⟨hx.1.1, hx.2⟩, fun x hx => hc'e ⟨hd.1.trans (not_le.1 hx.2), hx.1.2⟩⟩
+  /- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
+    done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
+    `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
+  cases' hc.2.eq_or_lt with heq hlt
+  · exact ⟨ec, HEq ▸ hec⟩
+  rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π E), Icc a d ⊆ e.baseSet
+  · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
+  /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
+    `d ∈ (c, b]`. -/
+  obtain ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, Ico c d ⊆ ec.base_set :=
+    (mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset hlt).1
+      (mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds ec.open_base_set (hec ⟨hc.1, le_rfl⟩))
+  have had : Ico a d ⊆ ec.base_set := Ico_subset_Icc_union_Ico.trans (union_subset hec hd)
+  by_cases he : Disjoint (Iio d) (Ioi c)
+  · /- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
+        Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
+        a trivialization over `[a, d]`. -/
+    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π E), d ∈ ed.baseSet :=
+      ⟨trivialization_at F E d, mem_base_set_trivialization_at F E d⟩
+    refine'
+      ⟨d, hdcb,
+        (ec.restr_open (Iio d) isOpen_Iio).disjointUnion (ed.restr_open (Ioi c) isOpen_Ioi)
+          (he.mono (inter_subset_right _ _) (inter_subset_right _ _)),
+        fun x hx => _⟩
+    rcases hx.2.eq_or_lt with (rfl | hxd)
+    exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
+  · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
+        `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
+    rw [disjoint_left] at he ; push_neg at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
+    exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
 
 end FiberBundle
@@ -997,9 +996,9 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
     where
   totalSpaceMk_inducing b := a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpaceMk_inducing b)
   trivializationAtlas :=
-    { e |
+    {e |
       ∃ (e₀ : _) (he₀ : e₀ ∈ a.pretrivializationAtlas),
-        e = a.trivializationOfMemPretrivializationAtlas he₀ }
+        e = a.trivializationOfMemPretrivializationAtlas he₀}
   trivializationAt x :=
     a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas x)
   mem_baseSet_trivializationAt := a.mem_base_pretrivializationAt

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

@@ -179,8 +179,8 @@ open TopologicalSpace Filter Set Bundle
 
 open scoped Topology Classical Bundle
 
-attribute [mfld_simps]
-  total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul total_space.mk_cast
+attribute [mfld_simps] total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul
+  total_space.mk_cast
 
 /-! ### General definition of fiber bundles -/
 
@@ -329,7 +329,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
       ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
     -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
       cases' le_or_lt a b with hab hab <;>
-      [skip;exact ⟨ea, by simp [*]⟩]
+      [skip; exact ⟨ea, by simp [*]⟩]
     /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
       We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
     set s : Set B := { x ∈ Icc a b | ∃ e : Trivialization F (π E), Icc a x ⊆ e.baseSet }
@@ -382,10 +382,10 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
             (he.mono (inter_subset_right _ _) (inter_subset_right _ _)),
           fun x hx => _⟩
       rcases hx.2.eq_or_lt with (rfl | hxd)
-      exacts[Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
+      exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
     · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
           `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
-      rw [disjoint_left] at he; push_neg  at he; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
+      rw [disjoint_left] at he ; push_neg  at he ; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
       exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
 
@@ -406,7 +406,7 @@ Trivialization changes from `i` to `j` are given by continuous maps `coord_chang
 space of continuous maps on `F`. -/
 @[nolint has_nonempty_instance]
 structure FiberBundleCore (ι : Type _) (B : Type _) [TopologicalSpace B] (F : Type _)
-  [TopologicalSpace F] where
+    [TopologicalSpace F] where
   baseSet : ι → Set B
   isOpen_baseSet : ∀ i, IsOpen (base_set i)
   indexAt : B → ι
@@ -496,13 +496,13 @@ def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
   map_target' p hp := by simpa using hp
   left_inv' := by
     rintro ⟨x, v⟩ hx
-    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx
+    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx 
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx.1
     · simp [hx]
   right_inv' := by
     rintro ⟨x, v⟩ hx
-    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx
+    simp only [prod_mk_mem_set_prod_eq, mem_inter_iff, and_true_iff, mem_univ] at hx 
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx.2
     · simp [hx]
@@ -541,14 +541,14 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
     simpa only [Set.mem_preimage, and_true_iff, Set.mem_univ, Set.mem_prod] using hp
   left_inv' := by
     rintro ⟨x, v⟩ hx
-    change x ∈ Z.base_set i at hx
+    change x ∈ Z.base_set i at hx 
     dsimp only
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact Z.mem_base_set_at _
     · simp only [hx, mem_inter_iff, and_self_iff, mem_base_set_at]
   right_inv' := by
     rintro ⟨x, v⟩ hx
-    simp only [prod_mk_mem_set_prod_eq, and_true_iff, mem_univ] at hx
+    simp only [prod_mk_mem_set_prod_eq, and_true_iff, mem_univ] at hx 
     rw [Z.coord_change_comp, Z.coord_change_self]
     · exact hx
     · simp only [hx, mem_inter_iff, and_self_iff, mem_base_set_at]
@@ -583,7 +583,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
     simp only [triv_change, local_triv_as_local_equiv, LocalEquiv.symm, true_and_iff,
       Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, LocalEquiv.trans_source, mem_inter_iff,
       and_true_iff, mem_preimage, proj, mem_univ, LocalEquiv.coe_mk, eq_self_iff_true,
-      LocalEquiv.coe_trans, total_space.proj] at hx⊢
+      LocalEquiv.coe_trans, total_space.proj] at hx ⊢
     simp only [Z.coord_change_comp, hx, mem_inter_iff, and_self_iff, mem_base_set_at]
 #align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_trans
 
@@ -631,7 +631,7 @@ def localTriv (i : ι) : Trivialization F Z.proj
     by
     apply continuousOn_open_of_generateFrom ((Z.is_open_base_set i).Prod isOpen_univ)
     intro t ht
-    simp only [exists_prop, mem_Union, mem_singleton_iff] at ht
+    simp only [exists_prop, mem_Union, mem_singleton_iff] at ht 
     obtain ⟨j, s, s_open, ts⟩ :
       ∃ j s,
         IsOpen s ∧
@@ -824,7 +824,7 @@ instance fiberBundle : FiberBundle F Z.Fiber
         rw [preimage_inter, ← preimage_comp, Function.comp]
         simp only [total_space_mk]
         refine' ext_iff.mpr fun a => ⟨fun ha => _, fun ha => ⟨Z.mem_base_set_at b, _⟩⟩
-        · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk] at ha
+        · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk] at ha 
           exact ha.2.2
         · simp only [mem_prod, mem_preimage, mem_inter_iff, local_triv_at_apply_mk]
           exact ⟨Z.mem_base_set_at b, ha⟩⟩
@@ -932,7 +932,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       rw [isOpen_coinduced, isOpen_induced_iff]
       obtain ⟨u, hu1, hu2⟩ := continuous_on_iff'.mp (a.continuous_triv_change _ he _ he') s hs
       have hu3 := congr_arg (fun s => (fun x : e'.target => (x : B × F)) ⁻¹' s) hu2
-      simp only [Subtype.coe_preimage_self, preimage_inter, univ_inter] at hu3
+      simp only [Subtype.coe_preimage_self, preimage_inter, univ_inter] at hu3 
       refine'
         ⟨u ∩ e'.to_local_equiv.target ∩ e'.to_local_equiv.symm ⁻¹' e.source, _, by
           simp only [preimage_inter, inter_univ, Subtype.coe_preimage_self, hu3.symm]; rfl⟩
@@ -975,7 +975,7 @@ theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
     @Inducing _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
   by
   letI := a.total_space_topology
-  rw [← restrict_comp_cod_restrict (a.mem_trivialization_at_source b)] at h
+  rw [← restrict_comp_cod_restrict (a.mem_trivialization_at_source b)] at h 
   apply Inducing.of_codRestrict (a.mem_trivialization_at_source b)
   refine'
     inducing_of_inducing_compose _
@@ -998,7 +998,7 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
   totalSpaceMk_inducing b := a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpaceMk_inducing b)
   trivializationAtlas :=
     { e |
-      ∃ (e₀ : _)(he₀ : e₀ ∈ a.pretrivializationAtlas),
+      ∃ (e₀ : _) (he₀ : e₀ ∈ a.pretrivializationAtlas),
         e = a.trivializationOfMemPretrivializationAtlas he₀ }
   trivializationAt x :=
     a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas x)

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

@@ -582,7 +582,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
   · rintro ⟨x, v⟩ hx
     simp only [triv_change, local_triv_as_local_equiv, LocalEquiv.symm, true_and_iff,
       Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, LocalEquiv.trans_source, mem_inter_iff,
-      and_true_iff, mem_preimage, proj, mem_univ, [anonymous], eq_self_iff_true,
+      and_true_iff, mem_preimage, proj, mem_univ, LocalEquiv.coe_mk, eq_self_iff_true,
       LocalEquiv.coe_trans, total_space.proj] at hx⊢
     simp only [Z.coord_change_comp, hx, mem_inter_iff, and_self_iff, mem_base_set_at]
 #align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_trans
@@ -853,6 +853,7 @@ end FiberBundleCore
 variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
   [∀ x, TopologicalSpace (E x)]
 
+#print FiberPrebundle /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
@@ -869,16 +870,19 @@ structure FiberPrebundle where
       ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
   totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ totalSpaceMk b)
 #align fiber_prebundle FiberPrebundle
+-/
 
 namespace FiberPrebundle
 
 variable {F E} (a : FiberPrebundle F E) {e : Pretrivialization F (π E)}
 
+#print FiberPrebundle.totalSpaceTopology /-
 /-- Topology on the total space that will make the prebundle into a bundle. -/
 def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E) :=
   ⨆ (e : Pretrivialization F (π E)) (he : e ∈ a.pretrivializationAtlas),
     coinduced e.setSymm Subtype.topologicalSpace
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
+-/
 
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
@@ -912,6 +916,7 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
   exact hu1.inter e'.open_target
 #align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter
 
+#print FiberPrebundle.trivializationOfMemPretrivializationAtlas /-
 /-- Promotion from a `pretrivialization` to a `trivialization`. -/
 def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @Trivialization B F _ _ _ a.totalSpaceTopology (π E) :=
@@ -935,6 +940,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       exact hu1.inter (a.is_open_target_of_mem_pretrivialization_atlas_inter e e' he')
     continuous_invFun := a.continuous_symm_of_mem_pretrivializationAtlas he }
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
+-/
 
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
     totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
@@ -980,6 +986,7 @@ theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
   exact (a.continuous_total_space_mk b).codRestrict (a.mem_trivialization_at_source b)
 #align fiber_prebundle.inducing_total_space_mk_of_inducing_comp FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp
 
+#print FiberPrebundle.toFiberBundle /-
 /-- Make a `fiber_bundle` from a `fiber_prebundle`.  Concretely this means
 that, given a `fiber_prebundle` structure for a sigma-type `E` -- which consists of a
 number of "pretrivializations" identifying parts of `E` with product spaces `U × F` -- one
@@ -998,6 +1005,7 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
   mem_baseSet_trivializationAt := a.mem_base_pretrivializationAt
   trivialization_mem_atlas x := ⟨_, a.pretrivialization_mem_atlas x, rfl⟩
 #align fiber_prebundle.to_fiber_bundle FiberPrebundle.toFiberBundle
+-/
 
 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit 0187644979f2d3e10a06e916a869c994facd9a87
+! leanprover-community/mathlib commit f7ebde7ee0d1505dfccac8644ae12371aa3c1c9f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -851,8 +851,8 @@ end FiberBundleCore
 
 
 variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
+  [∀ x, TopologicalSpace (E x)]
 
-#print FiberPrebundle /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
@@ -867,20 +867,18 @@ structure FiberPrebundle where
   continuous_triv_change :
     ∀ (e) (_ : e ∈ pretrivialization_atlas) (e') (_ : e' ∈ pretrivialization_atlas),
       ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
+  totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivialization_at b ∘ totalSpaceMk b)
 #align fiber_prebundle FiberPrebundle
--/
 
 namespace FiberPrebundle
 
 variable {F E} (a : FiberPrebundle F E) {e : Pretrivialization F (π E)}
 
-#print FiberPrebundle.totalSpaceTopology /-
 /-- Topology on the total space that will make the prebundle into a bundle. -/
 def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E) :=
   ⨆ (e : Pretrivialization F (π E)) (he : e ∈ a.pretrivializationAtlas),
     coinduced e.setSymm Subtype.topologicalSpace
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
--/
 
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
@@ -914,7 +912,6 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
   exact hu1.inter e'.open_target
 #align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter
 
-#print FiberPrebundle.trivializationOfMemPretrivializationAtlas /-
 /-- Promotion from a `pretrivialization` to a `trivialization`. -/
 def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @Trivialization B F _ _ _ a.totalSpaceTopology (π E) :=
@@ -938,7 +935,6 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       exact hu1.inter (a.is_open_target_of_mem_pretrivialization_atlas_inter e e' he')
     continuous_invFun := a.continuous_symm_of_mem_pretrivializationAtlas he }
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
--/
 
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
     totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
@@ -958,37 +954,41 @@ theorem totalSpaceMk_preimage_source (b : B) :
   exact a.mem_base_pretrivialization_at b
 #align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_source
 
-#print FiberPrebundle.fiberTopology /-
-/-- Topology on the fibers `E b` induced by the map `E b → E.total_space`. -/
-def fiberTopology (b : B) : TopologicalSpace (E b) :=
-  TopologicalSpace.induced (totalSpaceMk b) a.totalSpaceTopology
-#align fiber_prebundle.fiber_topology FiberPrebundle.fiberTopology
--/
-
-@[continuity]
-theorem inducing_totalSpaceMk (b : B) :
-    @Inducing _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) := by
-  letI := a.total_space_topology; letI := a.fiber_topology b; exact ⟨rfl⟩
-#align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMk
-
 @[continuity]
-theorem continuous_totalSpaceMk (b : B) :
-    @Continuous _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) :=
+theorem continuous_totalSpaceMk (b : B) : @Continuous _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
   by
-  letI := a.total_space_topology; letI := a.fiber_topology b
-  exact (a.inducing_total_space_mk b).Continuous
+  letI := a.total_space_topology
+  let e := a.trivialization_of_mem_pretrivialization_atlas (a.pretrivialization_mem_atlas b)
+  rw [e.to_local_homeomorph.continuous_iff_continuous_comp_left
+      (a.total_space_mk_preimage_source b)]
+  exact continuous_iff_le_induced.mpr (le_antisymm_iff.mp (a.total_space_mk_inducing b).induced).1
 #align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMk
 
-#print FiberPrebundle.toFiberBundle /-
+theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
+    (h : Inducing (a.pretrivializationAt b ∘ totalSpaceMk b)) :
+    @Inducing _ _ _ a.totalSpaceTopology (totalSpaceMk b) :=
+  by
+  letI := a.total_space_topology
+  rw [← restrict_comp_cod_restrict (a.mem_trivialization_at_source b)] at h
+  apply Inducing.of_codRestrict (a.mem_trivialization_at_source b)
+  refine'
+    inducing_of_inducing_compose _
+      (continuous_on_iff_continuous_restrict.mp
+        (a.trivialization_of_mem_pretrivialization_atlas
+            (a.pretrivialization_mem_atlas b)).continuous_toFun)
+      h
+  exact (a.continuous_total_space_mk b).codRestrict (a.mem_trivialization_at_source b)
+#align fiber_prebundle.inducing_total_space_mk_of_inducing_comp FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp
+
 /-- Make a `fiber_bundle` from a `fiber_prebundle`.  Concretely this means
 that, given a `fiber_prebundle` structure for a sigma-type `E` -- which consists of a
 number of "pretrivializations" identifying parts of `E` with product spaces `U × F` -- one
 establishes that for the topology constructed on the sigma-type using
 `fiber_prebundle.total_space_topology`, these "pretrivializations" are actually
 "trivializations" (i.e., homeomorphisms with respect to the constructed topology). -/
-def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology
+def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _
     where
-  totalSpaceMk_inducing := a.inducing_totalSpaceMk
+  totalSpaceMk_inducing b := a.inducing_totalSpaceMk_of_inducing_comp b (a.totalSpaceMk_inducing b)
   trivializationAtlas :=
     { e |
       ∃ (e₀ : _)(he₀ : e₀ ∈ a.pretrivializationAtlas),
@@ -998,12 +998,10 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology
   mem_baseSet_trivializationAt := a.mem_base_pretrivializationAt
   trivialization_mem_atlas x := ⟨_, a.pretrivialization_mem_atlas x, rfl⟩
 #align fiber_prebundle.to_fiber_bundle FiberPrebundle.toFiberBundle
--/
 
 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   by
   letI := a.total_space_topology
-  letI := a.fiber_topology
   letI := a.to_fiber_bundle
   exact continuous_proj F E
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj

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

@@ -177,7 +177,7 @@ variable {ι B F X : Type _} [TopologicalSpace X]
 
 open TopologicalSpace Filter Set Bundle
 
-open Topology Classical Bundle
+open scoped Topology Classical Bundle
 
 attribute [mfld_simps]
   total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul total_space.mk_cast

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

@@ -231,12 +231,6 @@ namespace FiberBundle
 
 variable (F) {E} [FiberBundle F E]
 
-/- warning: fiber_bundle.map_proj_nhds -> FiberBundle.map_proj_nhds is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] {E : B -> Type.{u3}} [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : Bundle.TotalSpace.{u1, u3} B E), Eq.{succ u1} (Filter.{u1} B) (Filter.map.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) (nhds.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) _inst_4 x)) (nhds.{u1} B _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E x))
-but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] {E : B -> Type.{u1}} [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : Bundle.TotalSpace.{u2, u1} B E), Eq.{succ u2} (Filter.{u2} B) (Filter.map.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E) (nhds.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B E) _inst_4 x)) (nhds.{u2} B _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E x))
-Case conversion may be inaccurate. Consider using '#align fiber_bundle.map_proj_nhds FiberBundle.map_proj_nhdsₓ'. -/
 theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
   (trivializationAt F E x.proj).map_proj_nhds <|
     (trivializationAt F E x.proj).mem_source.2 <| mem_baseSet_trivializationAt F E x.proj
@@ -244,35 +238,17 @@ theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
 
 variable (E)
 
-/- warning: fiber_bundle.continuous_proj -> FiberBundle.continuous_proj is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
-but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], Continuous.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)
-Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_proj FiberBundle.continuous_projₓ'. -/
 /-- The projection from a fiber bundle to its base is continuous. -/
 @[continuity]
 theorem continuous_proj : Continuous (π E) :=
   continuous_iff_continuousAt.2 fun x => (map_proj_nhds F x).le
 #align fiber_bundle.continuous_proj FiberBundle.continuous_proj
 
-/- warning: fiber_bundle.is_open_map_proj -> FiberBundle.isOpenMap_proj is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], IsOpenMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
-but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], IsOpenMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)
-Case conversion may be inaccurate. Consider using '#align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_projₓ'. -/
 /-- The projection from a fiber bundle to its base is an open map. -/
 theorem isOpenMap_proj : IsOpenMap (π E) :=
   IsOpenMap.of_nhds_le fun x => (map_proj_nhds F x).ge
 #align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_proj
 
-/- warning: fiber_bundle.surjective_proj -> FiberBundle.surjective_proj is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u2} F], Function.Surjective.{max (succ u1) (succ u3), succ u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E)
-but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u3} F], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E)
-Case conversion may be inaccurate. Consider using '#align fiber_bundle.surjective_proj FiberBundle.surjective_projₓ'. -/
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a surjective
 map. -/
 theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
@@ -281,48 +257,24 @@ theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
   ⟨p, hpb⟩
 #align fiber_bundle.surjective_proj FiberBundle.surjective_proj
 
-/- warning: fiber_bundle.quotient_map_proj -> FiberBundle.quotientMap_proj is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u2} F], QuotientMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
-but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u3} F], QuotientMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)
-Case conversion may be inaccurate. Consider using '#align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_projₓ'. -/
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a quotient
 map. -/
 theorem quotientMap_proj [Nonempty F] : QuotientMap (π E) :=
   (isOpenMap_proj F E).to_quotientMap (continuous_proj F E) (surjective_proj F E)
 #align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_proj
 
-/- warning: fiber_bundle.continuous_total_space_mk -> FiberBundle.continuous_totalSpaceMk is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : B), Continuous.{u3, max u1 u3} (E x) (Bundle.TotalSpace.{u1, u3} B E) (_inst_5 x) _inst_4 (Bundle.totalSpaceMk.{u1, u3} B E x)
-but is expected to have type
-  forall {B : Type.{u1}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u2}) [_inst_4 : TopologicalSpace.{max u2 u1} (Bundle.TotalSpace.{u1, u2} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u2} (E b)] [_inst_6 : FiberBundle.{u1, u3, u2} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : B), Continuous.{u2, max u1 u2} (E x) (Bundle.TotalSpace.{u1, u2} B E) (_inst_5 x) _inst_4 (Bundle.totalSpaceMk.{u1, u2} B E x)
-Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMkₓ'. -/
 theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
   (totalSpaceMk_inducing F E x).Continuous
 #align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMk
 
 variable {E F}
 
-/- warning: fiber_bundle.mem_trivialization_at_proj_source -> FiberBundle.mem_trivializationAt_proj_source is a dubious translation:
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 @[simp, mfld_simps]
 theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
     x ∈ (trivializationAt F E x.proj).source :=
   (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
 
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 @[simp, mfld_simps]
 theorem trivializationAt_proj_fst {x : TotalSpace E} :
     ((trivializationAt F E x.proj) x).1 = x.proj :=
@@ -333,9 +285,6 @@ variable (F)
 
 open Trivialization
 
-/- warning: fiber_bundle.continuous_within_at_total_space -> FiberBundle.continuousWithinAt_totalSpace is a dubious translation:
-<too large>
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 /-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
 theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
     ContinuousWithinAt f s x₀ ↔
@@ -358,12 +307,6 @@ theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀
   · rwa [source_eq, preimage_preimage]
 #align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
 
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 /-- Characterization of continuous functions (at a point) into a fiber bundle. -/
 theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
     ContinuousAt f x₀ ↔
@@ -376,12 +319,6 @@ end FiberBundle
 
 variable (F E)
 
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 /-- If `E` is a fiber bundle over a conditionally complete linear order,
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
@@ -546,12 +483,6 @@ def proj : Z.TotalSpace → B :=
 #align fiber_bundle_core.proj FiberBundleCore.proj
 -/
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Local homeomorphism version of the trivialization change. -/
@@ -583,12 +514,6 @@ def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
       ContinuousOn.prod continuous_fst.continuous_on (Z.continuous_on_coord_change j i)
 #align fiber_bundle_core.triv_change FiberBundleCore.trivChange
 
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 @[simp, mfld_simps]
 theorem mem_trivChange_source (i j : ι) (p : B × F) :
     p ∈ (Z.trivChange i j).source ↔ p.1 ∈ Z.baseSet i ∩ Z.baseSet j := by erw [mem_prod]; simp
@@ -632,45 +557,21 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
 
 variable (i : ι)
 
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 theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
 
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 theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
     p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i := by erw [mem_prod];
   simp only [and_true_iff, mem_univ]
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_target
 
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 theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
     (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
 
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 /-- The composition of two local trivializations is the trivialization change Z.triv_change i j. -/
 theorem localTrivAsLocalEquiv_trans (i j : ι) :
     (Z.localTrivAsLocalEquiv i).symm.trans (Z.localTrivAsLocalEquiv j) ≈
@@ -697,12 +598,6 @@ instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace Z.Fiber) :=
 
 variable (b : B) (a : F)
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
   by
@@ -769,23 +664,11 @@ def localTrivAt (b : B) : Trivialization F (π Z.Fiber) :=
 #align fiber_bundle_core.local_triv_at FiberBundleCore.localTrivAt
 -/
 
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 @[simp, mfld_simps]
 theorem localTrivAt_def (b : B) : Z.localTriv (Z.indexAt b) = Z.localTrivAt b :=
   rfl
 #align fiber_bundle_core.local_triv_at_def FiberBundleCore.localTrivAt_def
 
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 /-- If an element of `F` is invariant under all coordinate changes, then one can define a
 corresponding section of the fiber bundle, which is continuous. This applies in particular to the
 zero section of a vector bundle. Another example (not yet defined) would be the identity
@@ -807,175 +690,85 @@ theorem continuous_const_section (v : F)
   · exact A
 #align fiber_bundle_core.continuous_const_section FiberBundleCore.continuous_const_section
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv i :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsLocalEquiv_coe
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_source :
     (Z.localTrivAsLocalEquiv i).source = (Z.localTriv i).source :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsLocalEquiv_source
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_target :
     (Z.localTrivAsLocalEquiv i).target = (Z.localTriv i).target :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsLocalEquiv_target
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_symm :
     (Z.localTrivAsLocalEquiv i).symm = (Z.localTriv i).toLocalEquiv.symm :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsLocalEquiv_symm
 
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 @[simp, mfld_simps]
 theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
   rfl
 #align fiber_bundle_core.base_set_at FiberBundleCore.baseSet_at
 
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 @[simp, mfld_simps]
 theorem localTriv_apply (p : Z.TotalSpace) :
     (Z.localTriv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_apply
 
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 @[simp, mfld_simps]
 theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
   rw [local_triv_at, local_triv_apply, coord_change_self]; exact Z.mem_base_set_at p.1
 #align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_apply
 
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 @[simp, mfld_simps]
 theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = ⟨b, a⟩ :=
   Z.localTrivAt_apply _
 #align fiber_bundle_core.local_triv_at_apply_mk FiberBundleCore.localTrivAt_apply_mk
 
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 @[simp, mfld_simps]
 theorem mem_localTriv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTriv i).source ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_source
 
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 @[simp, mfld_simps]
 theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
     p ∈ (Z.localTrivAt b).source ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_source
 
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 @[simp, mfld_simps]
 theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
   rw [local_triv_at, mem_local_triv_source]; exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
 
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 @[simp, mfld_simps]
 theorem mem_localTriv_target (p : B × F) :
     p ∈ (Z.localTriv i).target ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Trivialization.mem_target _
 #align fiber_bundle_core.mem_local_triv_target FiberBundleCore.mem_localTriv_target
 
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 @[simp, mfld_simps]
 theorem mem_localTrivAt_target (p : B × F) (b : B) :
     p ∈ (Z.localTrivAt b).target ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Trivialization.mem_target _
 #align fiber_bundle_core.mem_local_triv_at_target FiberBundleCore.mem_localTrivAt_target
 
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 @[simp, mfld_simps]
 theorem localTriv_symm_apply (p : B × F) :
     (Z.localTriv i).toLocalHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_apply
 
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 @[simp, mfld_simps]
 theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
   rw [local_triv_at, ← base_set_at]; exact Z.mem_base_set_at b
@@ -1042,23 +835,11 @@ instance fiberBundle : FiberBundle F Z.Fiber
 #align fiber_bundle_core.fiber_bundle FiberBundleCore.fiberBundle
 -/
 
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 /-- The projection on the base of a fiber bundle created from core is continuous -/
 theorem continuous_proj : Continuous Z.proj :=
   continuous_proj F Z.Fiber
 #align fiber_bundle_core.continuous_proj FiberBundleCore.continuous_proj
 
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 /-- The projection on the base of a fiber bundle created from core is an open map -/
 theorem isOpenMap_proj : IsOpenMap Z.proj :=
   isOpenMap_proj F Z.Fiber
@@ -1101,12 +882,6 @@ def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
 -/
 
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 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
   by
@@ -1116,12 +891,6 @@ theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializ
   exact le_iSup₂ e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
 
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 theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTopology] e.source :=
   by
   letI := a.total_space_topology
@@ -1133,12 +902,6 @@ theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTop
     Pretrivialization.preimage_symm_proj_inter]
 #align fiber_prebundle.is_open_source FiberPrebundle.isOpen_source
 
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-Case conversion may be inaccurate. Consider using '#align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_interₓ'. -/
 theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π E))
     (he' : e' ∈ a.pretrivializationAtlas) :
     IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) :=
@@ -1177,12 +940,6 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
 -/
 
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 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
     totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
   by
@@ -1190,12 +947,6 @@ theorem mem_pretrivializationAt_source (b : B) (x : E b) :
   exact a.mem_base_pretrivialization_at b
 #align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_pretrivializationAt_source
 
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 @[simp]
 theorem totalSpaceMk_preimage_source (b : B) :
     totalSpaceMk b ⁻¹' (a.pretrivializationAt b).source = univ :=
@@ -1214,24 +965,12 @@ def fiberTopology (b : B) : TopologicalSpace (E b) :=
 #align fiber_prebundle.fiber_topology FiberPrebundle.fiberTopology
 -/
 
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 @[continuity]
 theorem inducing_totalSpaceMk (b : B) :
     @Inducing _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) := by
   letI := a.total_space_topology; letI := a.fiber_topology b; exact ⟨rfl⟩
 #align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMk
 
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 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
     @Continuous _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) :=
@@ -1261,12 +1000,6 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology
 #align fiber_prebundle.to_fiber_bundle FiberPrebundle.toFiberBundle
 -/
 
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 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   by
   letI := a.total_space_topology
@@ -1275,12 +1008,6 @@ theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   exact continuous_proj F E
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj
 
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-  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_2 _inst_3) {X : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u3, u2} B E) -> X} {s : Set.{u3} B}, (IsOpen.{u3} B _inst_2 s) -> (forall (b : B), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b s) -> (ContinuousOn.{max u3 u1, u4} (Prod.{u3, u1} B F) X (instTopologicalSpaceProd.{u3, u1} B F _inst_2 _inst_3) _inst_4 (Function.comp.{succ (max u3 u1), max (succ u3) (succ u2), succ u4} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) X f (LocalEquiv.toFun.{max u3 u1, max u3 u2} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) (LocalEquiv.symm.{max u3 u2, max u3 u1} (Bundle.TotalSpace.{u3, u2} B E) (Prod.{u3, u1} B F) (Pretrivialization.toLocalEquiv.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_2 _inst_3 a b))))) (Set.prod.{u3, u1} B F (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) s (Pretrivialization.baseSet.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_2 _inst_3 a b))) (Set.univ.{u1} F)))) -> (ContinuousOn.{max u3 u2, u4} (Bundle.TotalSpace.{u3, u2} B E) X (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_2 _inst_3 a) _inst_4 f (Set.preimage.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (Bundle.TotalSpace.proj.{u3, u2} B E) s))
-Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_on_of_comp_right FiberPrebundle.continuousOn_of_comp_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- For a fiber bundle `E` over `B` constructed using the `fiber_prebundle` mechanism,
 continuity of a function `total_space E → X` on an open set `s` can be checked by precomposing at

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

@@ -369,9 +369,7 @@ theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
     ContinuousAt f x₀ ↔
       ContinuousAt (fun x => (f x).proj) x₀ ∧
         ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ :=
-  by
-  simp_rw [← continuousWithinAt_univ]
-  exact continuous_within_at_total_space F f
+  by simp_rw [← continuousWithinAt_univ]; exact continuous_within_at_total_space F f
 #align fiber_bundle.continuous_at_total_space FiberBundle.continuousAt_totalSpace
 
 end FiberBundle
@@ -407,8 +405,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
     obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
       by
-      cases' hc.1.eq_or_lt with heq hlt
-      · rwa [← HEq]
+      cases' hc.1.eq_or_lt with heq hlt; · rwa [← HEq]
       refine' ⟨hc, _⟩
       /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
           of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
@@ -451,9 +448,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
       exacts[Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
     · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
           `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
-      rw [disjoint_left] at he
-      push_neg  at he
-      rcases he with ⟨d', hdd' : d' < d, hd'c⟩
+      rw [disjoint_left] at he; push_neg  at he; rcases he with ⟨d', hdd' : d' < d, hd'c⟩
       exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset
 
@@ -596,10 +591,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_triv_change_source FiberBundleCore.mem_trivChange_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_trivChange_source (i j : ι) (p : B × F) :
-    p ∈ (Z.trivChange i j).source ↔ p.1 ∈ Z.baseSet i ∩ Z.baseSet j :=
-  by
-  erw [mem_prod]
-  simp
+    p ∈ (Z.trivChange i j).source ↔ p.1 ∈ Z.baseSet i ∩ Z.baseSet j := by erw [mem_prod]; simp
 #align fiber_bundle_core.mem_triv_change_source FiberBundleCore.mem_trivChange_source
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -658,9 +650,7 @@ but is expected to have type
   forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_2 F _inst_3 Z i))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_targetₓ'. -/
 theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
-    p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i :=
-  by
-  erw [mem_prod]
+    p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i := by erw [mem_prod];
   simp only [and_true_iff, mem_univ]
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_target
 
@@ -687,9 +677,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
       (Z.trivChange i j).toLocalEquiv :=
   by
   constructor
-  · ext x
-    simp only [mem_local_triv_as_local_equiv_target, mfld_simps]
-    rfl
+  · ext x; simp only [mem_local_triv_as_local_equiv_target, mfld_simps]; rfl
   · rintro ⟨x, v⟩ hx
     simp only [triv_change, local_triv_as_local_equiv, LocalEquiv.symm, true_and_iff,
       Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, LocalEquiv.trans_source, mem_inter_iff,
@@ -735,9 +723,7 @@ def localTriv (i : ι) : Trivialization F Z.proj
   open_baseSet := Z.isOpen_baseSet i
   source_eq := rfl
   target_eq := rfl
-  proj_toFun p hp := by
-    simp only [mfld_simps]
-    rfl
+  proj_toFun p hp := by simp only [mfld_simps]; rfl
   open_source := Z.open_source' i
   open_target := (Z.isOpen_baseSet i).Prod isOpen_univ
   continuous_toFun := by
@@ -898,10 +884,8 @@ but is expected to have type
   forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (Trivialization.toFun'.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_2 _inst_3 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p)) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_applyₓ'. -/
 @[simp, mfld_simps]
-theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ :=
-  by
-  rw [local_triv_at, local_triv_apply, coord_change_self]
-  exact Z.mem_base_set_at p.1
+theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ := by
+  rw [local_triv_at, local_triv_apply, coord_change_self]; exact Z.mem_base_set_at p.1
 #align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_apply
 
 /- warning: fiber_bundle_core.local_triv_at_apply_mk -> FiberBundleCore.localTrivAt_apply_mk is a dubious translation:
@@ -946,10 +930,8 @@ but is expected to have type
   forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (b : B) (a : F), Membership.mem.{max u3 u2, max u3 u2} (Sigma.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z x)) (Set.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z))) (Set.instMembershipSet.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z))) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z x) b a) (LocalEquiv.source.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b))))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_atₓ'. -/
 @[simp, mfld_simps]
-theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source :=
-  by
-  rw [local_triv_at, mem_local_triv_source]
-  exact Z.mem_base_set_at b
+theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
+  rw [local_triv_at, mem_local_triv_source]; exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
 
 /- warning: fiber_bundle_core.mem_local_triv_target -> FiberBundleCore.mem_localTriv_target is a dubious translation:
@@ -995,10 +977,8 @@ but is expected to have type
   forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (b : B), Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSetₓ'. -/
 @[simp, mfld_simps]
-theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet :=
-  by
-  rw [local_triv_at, ← base_set_at]
-  exact Z.mem_base_set_at b
+theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
+  rw [local_triv_at, ← base_set_at]; exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSet
 
 #print FiberBundleCore.continuous_totalSpaceMk /-
@@ -1017,10 +997,8 @@ theorem continuous_totalSpaceMk (b : B) :
   apply IsOpen.inter
   · simp only [total_space.proj, proj, ← preimage_comp]
     by_cases b ∈ (Z.local_triv i).baseSet
-    · rw [preimage_const_of_mem h]
-      exact isOpen_univ
-    · rw [preimage_const_of_not_mem h]
-      exact isOpen_empty
+    · rw [preimage_const_of_mem h]; exact isOpen_univ
+    · rw [preimage_const_of_not_mem h]; exact isOpen_empty
   · simp only [Function.comp, local_triv_apply]
     rw [preimage_inter, preimage_comp]
     by_cases b ∈ Z.base_set i
@@ -1183,9 +1161,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       letI := a.total_space_topology
       refine'
         continuous_on_iff'.mpr fun s hs =>
-          ⟨e ⁻¹' s ∩ e.source, is_open_supr_iff.mpr fun e' => _,
-            by
-            rw [inter_assoc, inter_self]
+          ⟨e ⁻¹' s ∩ e.source, is_open_supr_iff.mpr fun e' => _, by rw [inter_assoc, inter_self];
             rfl⟩
       refine' is_open_supr_iff.mpr fun he' => _
       rw [isOpen_coinduced, isOpen_induced_iff]
@@ -1193,10 +1169,8 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       have hu3 := congr_arg (fun s => (fun x : e'.target => (x : B × F)) ⁻¹' s) hu2
       simp only [Subtype.coe_preimage_self, preimage_inter, univ_inter] at hu3
       refine'
-        ⟨u ∩ e'.to_local_equiv.target ∩ e'.to_local_equiv.symm ⁻¹' e.source, _,
-          by
-          simp only [preimage_inter, inter_univ, Subtype.coe_preimage_self, hu3.symm]
-          rfl⟩
+        ⟨u ∩ e'.to_local_equiv.target ∩ e'.to_local_equiv.symm ⁻¹' e.source, _, by
+          simp only [preimage_inter, inter_univ, Subtype.coe_preimage_self, hu3.symm]; rfl⟩
       rw [inter_assoc]
       exact hu1.inter (a.is_open_target_of_mem_pretrivialization_atlas_inter e e' he')
     continuous_invFun := a.continuous_symm_of_mem_pretrivializationAtlas he }
@@ -1248,11 +1222,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMkₓ'. -/
 @[continuity]
 theorem inducing_totalSpaceMk (b : B) :
-    @Inducing _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) :=
-  by
-  letI := a.total_space_topology
-  letI := a.fiber_topology b
-  exact ⟨rfl⟩
+    @Inducing _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) := by
+  letI := a.total_space_topology; letI := a.fiber_topology b; exact ⟨rfl⟩
 #align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMk
 
 /- warning: fiber_prebundle.continuous_total_space_mk -> FiberPrebundle.continuous_totalSpaceMk is a dubious translation:

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

@@ -334,10 +334,7 @@ variable (F)
 open Trivialization
 
 /- warning: fiber_bundle.continuous_within_at_total_space -> FiberBundle.continuousWithinAt_totalSpace is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpaceₓ'. -/
 /-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
 theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -397,7 +397,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
       ⟨trivialization_at F E a, mem_base_set_trivialization_at F E a⟩
     -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
       cases' le_or_lt a b with hab hab <;>
-      [skip, exact ⟨ea, by simp [*]⟩]
+      [skip;exact ⟨ea, by simp [*]⟩]
     /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
       We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
     set s : Set B := { x ∈ Icc a b | ∃ e : Trivialization F (π E), Icc a x ⊆ e.baseSet }

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

@@ -406,7 +406,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
     have sbd : BddAbove s := ⟨b, hsb⟩
     set c := Sup s
-    have hsc : IsLUB s c := isLUB_csupₛ sne sbd
+    have hsc : IsLUB s c := isLUB_csSup sne sbd
     have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
     obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.base_set⟩ : c ∈ s :=
       by
@@ -1138,7 +1138,7 @@ theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializ
   refine'
     id fun z H =>
       id fun U h => preimage_nhdsWithin_coinduced' H e.open_target (le_def.1 (nhds_mono _) U h)
-  exact le_supᵢ₂ e he
+  exact le_iSup₂ e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
 
 /- warning: fiber_prebundle.is_open_source -> FiberPrebundle.isOpen_source is a dubious translation:

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

@@ -305,12 +305,24 @@ theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
 
 variable {E F}
 
+/- warning: fiber_bundle.mem_trivialization_at_proj_source -> FiberBundle.mem_trivializationAt_proj_source is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] {E : B -> Type.{u3}} [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] {x : Bundle.TotalSpace.{u1, u3} B E}, 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)) x (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_2 _inst_3) (Trivialization.toLocalHomeomorph.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) (FiberBundle.trivializationAt.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b) _inst_6 (Bundle.TotalSpace.proj.{u1, u3} B E x)))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
     x ∈ (trivializationAt F E x.proj).source :=
   (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
 
+/- warning: fiber_bundle.trivialization_at_proj_fst -> FiberBundle.trivializationAt_proj_fst is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] {E : B -> Type.{u3}} [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] {x : Bundle.TotalSpace.{u1, u3} B 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_2 _inst_3 _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_2 _inst_3 _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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) _inst_4) (FiberBundle.trivializationAt.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b) _inst_6 (Bundle.TotalSpace.proj.{u1, u3} B E x)) x)) (Bundle.TotalSpace.proj.{u1, u3} B E x)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle.trivialization_at_proj_fst FiberBundle.trivializationAt_proj_fstₓ'. -/
 @[simp, mfld_simps]
 theorem trivializationAt_proj_fst {x : TotalSpace E} :
     ((trivializationAt F E x.proj) x).1 = x.proj :=
@@ -321,6 +333,12 @@ variable (F)
 
 open Trivialization
 
+/- warning: fiber_bundle.continuous_within_at_total_space -> FiberBundle.continuousWithinAt_totalSpace is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) {X : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} X] [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] {E : B -> Type.{u4}} [_inst_4 : TopologicalSpace.{max u1 u4} (Bundle.TotalSpace.{u1, u4} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u4} (E b)] [_inst_6 : FiberBundle.{u1, u2, u4} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (f : X -> (Bundle.TotalSpace.{u1, u4} B E)) {s : Set.{u3} X} {x₀ : X}, Iff (ContinuousWithinAt.{u3, max u1 u4} X (Bundle.TotalSpace.{u1, u4} B E) _inst_1 _inst_4 f s x₀) (And (ContinuousWithinAt.{u3, u1} X B _inst_1 _inst_2 (fun (x : X) => Bundle.TotalSpace.proj.{u1, u4} B E (f x)) s x₀) (ContinuousWithinAt.{u3, u2} X F _inst_1 _inst_3 (fun (x : X) => Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u4)), max (succ (max u1 u4)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u4} B F (Bundle.TotalSpace.{u1, u4} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u4} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u4} B F (Bundle.TotalSpace.{u1, u4} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u4} B E)) => (Bundle.TotalSpace.{u1, u4} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u4} B F (Bundle.TotalSpace.{u1, u4} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u4} B E) _inst_4) (FiberBundle.trivializationAt.{u1, u2, u4} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b) _inst_6 (Bundle.TotalSpace.proj.{u1, u4} B E (f x₀))) (f x))) s x₀))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpaceₓ'. -/
 /-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
 theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
     ContinuousWithinAt f s x₀ ↔
@@ -343,6 +361,12 @@ theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀
   · rwa [source_eq, preimage_preimage]
 #align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
 
+/- warning: fiber_bundle.continuous_at_total_space -> FiberBundle.continuousAt_totalSpace is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) {X : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} X] [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] {E : B -> Type.{u4}} [_inst_4 : TopologicalSpace.{max u1 u4} (Bundle.TotalSpace.{u1, u4} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u4} (E b)] [_inst_6 : FiberBundle.{u1, u2, u4} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (f : X -> (Bundle.TotalSpace.{u1, u4} B E)) {x₀ : X}, Iff (ContinuousAt.{u3, max u1 u4} X (Bundle.TotalSpace.{u1, u4} B E) _inst_1 _inst_4 f x₀) (And (ContinuousAt.{u3, u1} X B _inst_1 _inst_2 (fun (x : X) => Bundle.TotalSpace.proj.{u1, u4} B E (f x)) x₀) (ContinuousAt.{u3, u2} X F _inst_1 _inst_3 (fun (x : X) => Prod.snd.{u1, u2} B F (coeFn.{max (succ u1) (succ u2) (succ (max u1 u4)), max (succ (max u1 u4)) (succ u1) (succ u2)} (Trivialization.{u1, u2, max u1 u4} B F (Bundle.TotalSpace.{u1, u4} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u4} B E)) (fun (_x : Trivialization.{u1, u2, max u1 u4} B F (Bundle.TotalSpace.{u1, u4} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u4} B E)) => (Bundle.TotalSpace.{u1, u4} B E) -> (Prod.{u1, u2} B F)) (Trivialization.hasCoeToFun.{u1, u2, max u1 u4} B F (Bundle.TotalSpace.{u1, u4} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u4} B E) _inst_4) (FiberBundle.trivializationAt.{u1, u2, u4} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b) _inst_6 (Bundle.TotalSpace.proj.{u1, u4} B E (f x₀))) (f x))) x₀))
+but is expected to have type
+  forall {B : Type.{u4}} (F : Type.{u1}) {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u4} B] [_inst_3 : TopologicalSpace.{u1} F] {E : B -> Type.{u3}} [_inst_4 : TopologicalSpace.{max u3 u4} (Bundle.TotalSpace.{u4, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u4, u1, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (f : X -> (Bundle.TotalSpace.{u4, u3} B E)) {x₀ : X}, Iff (ContinuousAt.{u2, max u4 u3} X (Bundle.TotalSpace.{u4, u3} B E) _inst_1 _inst_4 f x₀) (And (ContinuousAt.{u2, u4} X B _inst_1 _inst_2 (fun (x : X) => Bundle.TotalSpace.proj.{u4, u3} B E (f x)) x₀) (ContinuousAt.{u2, u1} X F _inst_1 _inst_3 (fun (x : X) => Prod.snd.{u4, u1} B F (Trivialization.toFun'.{u4, u1, max u4 u3} B F (Bundle.TotalSpace.{u4, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u4, u3} B E) _inst_4 (FiberBundle.trivializationAt.{u4, u1, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b) _inst_6 (Bundle.TotalSpace.proj.{u4, u3} B E (f x₀))) (f x))) x₀))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_at_total_space FiberBundle.continuousAt_totalSpaceₓ'. -/
 /-- Characterization of continuous functions (at a point) into a fiber bundle. -/
 theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
     ContinuousAt f x₀ ↔

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

@@ -191,11 +191,11 @@ variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace E)] [∀ b, TopologicalSpace (E b)]
 
 #print FiberBundle /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_baseSet_trivializationAt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`trivialization_mem_atlas] [] -/
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit 8ef6f08ff8c781c5c07a8b12843710e1a0d8a688
+! leanprover-community/mathlib commit 0187644979f2d3e10a06e916a869c994facd9a87
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -173,14 +173,14 @@ Fiber bundle, topological bundle, structure group
 -/
 
 
-variable {ι : Type _} {B : Type _} {F : Type _}
+variable {ι B F X : Type _} [TopologicalSpace X]
 
 open TopologicalSpace Filter Set Bundle
 
 open Topology Classical Bundle
 
 attribute [mfld_simps]
-  total_space.proj total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul total_space.mk_cast
+  total_space_mk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul total_space.mk_cast
 
 /-! ### General definition of fiber bundles -/
 
@@ -233,9 +233,9 @@ variable (F) {E} [FiberBundle F E]
 
 /- warning: fiber_bundle.map_proj_nhds -> FiberBundle.map_proj_nhds is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {E : B -> Type.{u3}} [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : Bundle.TotalSpace.{u1, u3} B E), Eq.{succ u1} (Filter.{u1} B) (Filter.map.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) (nhds.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) _inst_3 x)) (nhds.{u1} B _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E x))
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] {E : B -> Type.{u3}} [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : Bundle.TotalSpace.{u1, u3} B E), Eq.{succ u1} (Filter.{u1} B) (Filter.map.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) (nhds.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) _inst_4 x)) (nhds.{u1} B _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E x))
 but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] {E : B -> Type.{u1}} [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : Bundle.TotalSpace.{u2, u1} B E), Eq.{succ u2} (Filter.{u2} B) (Filter.map.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E) (nhds.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B E) _inst_3 x)) (nhds.{u2} B _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E x))
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] {E : B -> Type.{u1}} [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : Bundle.TotalSpace.{u2, u1} B E), Eq.{succ u2} (Filter.{u2} B) (Filter.map.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E) (nhds.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B E) _inst_4 x)) (nhds.{u2} B _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E x))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.map_proj_nhds FiberBundle.map_proj_nhdsₓ'. -/
 theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
   (trivializationAt F E x.proj).map_proj_nhds <|
@@ -246,9 +246,9 @@ variable (E)
 
 /- warning: fiber_bundle.continuous_proj -> FiberBundle.continuous_proj is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
 but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], Continuous.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E)
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], Continuous.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_proj FiberBundle.continuous_projₓ'. -/
 /-- The projection from a fiber bundle to its base is continuous. -/
 @[continuity]
@@ -258,9 +258,9 @@ theorem continuous_proj : Continuous (π E) :=
 
 /- warning: fiber_bundle.is_open_map_proj -> FiberBundle.isOpenMap_proj is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], IsOpenMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], IsOpenMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
 but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], IsOpenMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E)
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)], IsOpenMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_projₓ'. -/
 /-- The projection from a fiber bundle to its base is an open map. -/
 theorem isOpenMap_proj : IsOpenMap (π E) :=
@@ -269,9 +269,9 @@ theorem isOpenMap_proj : IsOpenMap (π E) :=
 
 /- warning: fiber_bundle.surjective_proj -> FiberBundle.surjective_proj is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u2} F], Function.Surjective.{max (succ u1) (succ u3), succ u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E)
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u2} F], Function.Surjective.{max (succ u1) (succ u3), succ u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E)
 but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u3} F], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E)
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u3} F], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.surjective_proj FiberBundle.surjective_projₓ'. -/
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a surjective
 map. -/
@@ -283,9 +283,9 @@ theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
 
 /- warning: fiber_bundle.quotient_map_proj -> FiberBundle.quotientMap_proj is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u2} F], QuotientMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u2} F], QuotientMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
 but is expected to have type
-  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u3} F], QuotientMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E)
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : FiberBundle.{u2, u3, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] [_inst_7 : Nonempty.{succ u3} F], QuotientMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_4 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B E)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_projₓ'. -/
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a quotient
 map. -/
@@ -295,23 +295,73 @@ theorem quotientMap_proj [Nonempty F] : QuotientMap (π E) :=
 
 /- warning: fiber_bundle.continuous_total_space_mk -> FiberBundle.continuous_totalSpaceMk is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : B), Continuous.{u3, max u1 u3} (E x) (Bundle.TotalSpace.{u1, u3} B E) (_inst_4 x) _inst_3 (Bundle.totalSpaceMk.{u1, u3} B E x)
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : B), Continuous.{u3, max u1 u3} (E x) (Bundle.TotalSpace.{u1, u3} B E) (_inst_5 x) _inst_4 (Bundle.totalSpaceMk.{u1, u3} B E x)
 but is expected to have type
-  forall {B : Type.{u1}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u2}) [_inst_3 : TopologicalSpace.{max u2 u1} (Bundle.TotalSpace.{u1, u2} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u2} (E b)] [_inst_5 : FiberBundle.{u1, u3, u2} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : B), Continuous.{u2, max u1 u2} (E x) (Bundle.TotalSpace.{u1, u2} B E) (_inst_4 x) _inst_3 (Bundle.totalSpaceMk.{u1, u2} B E x)
+  forall {B : Type.{u1}} (F : Type.{u3}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u3} F] (E : B -> Type.{u2}) [_inst_4 : TopologicalSpace.{max u2 u1} (Bundle.TotalSpace.{u1, u2} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u2} (E b)] [_inst_6 : FiberBundle.{u1, u3, u2} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (x : B), Continuous.{u2, max u1 u2} (E x) (Bundle.TotalSpace.{u1, u2} B E) (_inst_5 x) _inst_4 (Bundle.totalSpaceMk.{u1, u2} B E x)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMkₓ'. -/
 theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
   (totalSpaceMk_inducing F E x).Continuous
 #align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMk
 
+variable {E F}
+
+@[simp, mfld_simps]
+theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
+    x ∈ (trivializationAt F E x.proj).source :=
+  (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
+#align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
+
+@[simp, mfld_simps]
+theorem trivializationAt_proj_fst {x : TotalSpace E} :
+    ((trivializationAt F E x.proj) x).1 = x.proj :=
+  Trivialization.coe_fst' _ <| mem_baseSet_trivializationAt F E x.proj
+#align fiber_bundle.trivialization_at_proj_fst FiberBundle.trivializationAt_proj_fst
+
+variable (F)
+
+open Trivialization
+
+/-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
+theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
+    ContinuousWithinAt f s x₀ ↔
+      ContinuousWithinAt (fun x => (f x).proj) s x₀ ∧
+        ContinuousWithinAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) s x₀ :=
+  by
+  refine' (and_iff_right_iff_imp.2 fun hf => _).symm.trans (and_congr_right fun hf => _)
+  · refine' (continuous_proj F E).ContinuousWithinAt.comp hf (maps_to_image f s)
+  have h1 : (fun x => (f x).proj) ⁻¹' (trivialization_at F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
+    hf.preimage_mem_nhds_within ((open_base_set _).mem_nhds (mem_base_set_trivialization_at F E _))
+  have h2 : ContinuousWithinAt (fun x => (trivialization_at F E (f x₀).proj (f x)).1) s x₀ :=
+    by
+    refine'
+      hf.congr_of_eventually_eq (eventually_of_mem h1 fun x hx => _) trivialization_at_proj_fst
+    rw [coe_fst']
+    exact hx
+  rw [(trivialization_at F E (f x₀).proj).continuousWithinAt_iff_continuousWithinAt_comp_left]
+  · simp_rw [continuousWithinAt_prod_iff, Function.comp, Trivialization.coe_coe, h2, true_and_iff]
+  · apply mem_trivialization_at_proj_source
+  · rwa [source_eq, preimage_preimage]
+#align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
+
+/-- Characterization of continuous functions (at a point) into a fiber bundle. -/
+theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
+    ContinuousAt f x₀ ↔
+      ContinuousAt (fun x => (f x).proj) x₀ ∧
+        ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ :=
+  by
+  simp_rw [← continuousWithinAt_univ]
+  exact continuous_within_at_total_space F f
+#align fiber_bundle.continuous_at_total_space FiberBundle.continuousAt_totalSpace
+
 end FiberBundle
 
 variable (F E)
 
 /- warning: fiber_bundle.exists_trivialization_Icc_subset -> FiberBundle.exists_trivialization_Icc_subset is a dubious translation:
 lean 3 declaration is
-  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : ConditionallyCompleteLinearOrder.{u1} B] [_inst_6 : OrderTopology.{u1} B _inst_1 (PartialOrder.toPreorder.{u1} B (SemilatticeInf.toPartialOrder.{u1} B (Lattice.toSemilatticeInf.{u1} B (ConditionallyCompleteLattice.toLattice.{u1} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} B _inst_5)))))] [_inst_7 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (a : B) (b : B), Exists.{max (succ u1) (succ u2) (succ (max u1 u3))} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) => HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) (Set.Icc.{u1} B (PartialOrder.toPreorder.{u1} B (SemilatticeInf.toPartialOrder.{u1} B (Lattice.toSemilatticeInf.{u1} B (ConditionallyCompleteLattice.toLattice.{u1} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} B _inst_5))))) a b) (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e))
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_6 : ConditionallyCompleteLinearOrder.{u1} B] [_inst_7 : OrderTopology.{u1} B _inst_2 (PartialOrder.toPreorder.{u1} B (SemilatticeInf.toPartialOrder.{u1} B (Lattice.toSemilatticeInf.{u1} B (ConditionallyCompleteLattice.toLattice.{u1} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} B _inst_6)))))] [_inst_8 : FiberBundle.{u1, u2, u3} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (a : B) (b : B), Exists.{max (succ u1) (succ u2) (succ (max u1 u3))} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E)) => HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) (Set.Icc.{u1} B (PartialOrder.toPreorder.{u1} B (SemilatticeInf.toPartialOrder.{u1} B (Lattice.toSemilatticeInf.{u1} B (ConditionallyCompleteLattice.toLattice.{u1} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} B _inst_6))))) a b) (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u1, u3} B E) e))
 but is expected to have type
-  forall {B : Type.{u3}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : ConditionallyCompleteLinearOrder.{u3} B] [_inst_6 : OrderTopology.{u3} B _inst_1 (PartialOrder.toPreorder.{u3} B (SemilatticeInf.toPartialOrder.{u3} B (Lattice.toSemilatticeInf.{u3} B (ConditionallyCompleteLattice.toLattice.{u3} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} B _inst_5)))))] [_inst_7 : FiberBundle.{u3, u2, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (a : B) (b : B), Exists.{max (max (succ u3) (succ u2)) (succ u1)} (Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) (fun (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) => HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) (Set.Icc.{u3} B (PartialOrder.toPreorder.{u3} B (SemilatticeInf.toPartialOrder.{u3} B (Lattice.toSemilatticeInf.{u3} B (ConditionallyCompleteLattice.toLattice.{u3} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} B _inst_5))))) a b) (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e))
+  forall {B : Type.{u3}} (F : Type.{u2}) [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (E : B -> Type.{u1}) [_inst_4 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_5 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_6 : ConditionallyCompleteLinearOrder.{u3} B] [_inst_7 : OrderTopology.{u3} B _inst_2 (PartialOrder.toPreorder.{u3} B (SemilatticeInf.toPartialOrder.{u3} B (Lattice.toSemilatticeInf.{u3} B (ConditionallyCompleteLattice.toLattice.{u3} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} B _inst_6)))))] [_inst_8 : FiberBundle.{u3, u2, u1} B F _inst_2 _inst_3 E _inst_4 (fun (b : B) => _inst_5 b)] (a : B) (b : B), Exists.{max (max (succ u3) (succ u2)) (succ u1)} (Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)) (fun (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E)) => HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) (Set.Icc.{u3} B (PartialOrder.toPreorder.{u3} B (SemilatticeInf.toPartialOrder.{u3} B (Lattice.toSemilatticeInf.{u3} B (ConditionallyCompleteLattice.toLattice.{u3} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} B _inst_6))))) a b) (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 _inst_4 (Bundle.TotalSpace.proj.{u3, u1} B E) e))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subsetₓ'. -/
 /-- If `E` is a fiber bundle over a conditionally complete linear order,
 then it is trivial over any closed interval. -/
@@ -482,9 +532,9 @@ def proj : Z.TotalSpace → B :=
 
 /- warning: fiber_bundle_core.triv_change -> FiberBundleCore.trivChange is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F], (FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) -> ι -> ι -> (LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F], (FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) -> ι -> ι -> (LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F], (FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) -> ι -> ι -> (LocalHomeomorph.{max u3 u2, max u3 u2} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (instTopologicalSpaceProd.{u2, u3} B F _inst_1 _inst_2) (instTopologicalSpaceProd.{u2, u3} B F _inst_1 _inst_2))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F], (FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) -> ι -> ι -> (LocalHomeomorph.{max u3 u2, max u3 u2} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (instTopologicalSpaceProd.{u2, u3} B F _inst_2 _inst_3) (instTopologicalSpaceProd.{u2, u3} B F _inst_2 _inst_3))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.triv_change FiberBundleCore.trivChangeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -519,9 +569,9 @@ def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
 
 /- warning: fiber_bundle_core.mem_triv_change_source -> FiberBundleCore.mem_trivChange_source is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (j : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i j)))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Inter.inter.{u2} (Set.{u2} B) (Set.hasInter.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z j)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (j : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (FiberBundleCore.trivChange.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i j)))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Inter.inter.{u2} (Set.{u2} B) (Set.hasInter.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z j)))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (j : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.source.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i j)))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_1 F _inst_2 Z i) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_1 F _inst_2 Z j)))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι) (j : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.source.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (FiberBundleCore.trivChange.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i j)))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_2 F _inst_3 Z i) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_2 F _inst_3 Z j)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_triv_change_source FiberBundleCore.mem_trivChange_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_trivChange_source (i j : ι) (p : B × F) :
@@ -571,9 +621,9 @@ variable (i : ι)
 
 /- warning: fiber_bundle_core.mem_local_triv_as_local_equiv_source -> FiberBundleCore.mem_localTrivAsLocalEquiv_source is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Set.hasMem.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Set.hasMem.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i))
 but is expected to have type
-  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Set.instMembershipSet.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) p (LocalEquiv.source.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u1} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.baseSet.{u3, u2, u1} ι B _inst_1 F _inst_2 Z i))
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Set.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (Set.instMembershipSet.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) p (LocalEquiv.source.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u1} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u3, u2, u1} ι B F _inst_2 _inst_3 Z i))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (FiberBundleCore.baseSet.{u3, u2, u1} ι B _inst_2 F _inst_3 Z i))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_sourceₓ'. -/
 theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
@@ -582,9 +632,9 @@ theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
 
 /- warning: fiber_bundle_core.mem_local_triv_as_local_equiv_target -> FiberBundleCore.mem_localTrivAsLocalEquiv_target is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_1 F _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_2 F _inst_3 Z i))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_targetₓ'. -/
 theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
     p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i :=
@@ -595,9 +645,9 @@ theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
 
 /- warning: fiber_bundle_core.local_triv_as_local_equiv_apply -> FiberBundleCore.localTrivAsLocalEquiv_apply is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} B F) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F)) (fun (_x : LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) -> (Prod.{u2, u3} B F)) (LocalEquiv.hasCoeToFun.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i) p) (Prod.mk.{u2, u3} B F (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_1 F _inst_2 Z (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_1 F _inst_2 Z (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p)) i (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (Sigma.snd.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} B F) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F)) (fun (_x : LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) -> (Prod.{u2, u3} B F)) (LocalEquiv.hasCoeToFun.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i) p) (Prod.mk.{u2, u3} B F (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_2 F _inst_3 Z (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_2 F _inst_3 Z (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p)) i (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p)))
 but is expected to have type
-  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (LocalEquiv.toFun.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u1} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.coordChange.{u3, u2, u1} ι B _inst_1 F _inst_2 Z (FiberBundleCore.indexAt.{u3, u2, u1} ι B _inst_1 F _inst_2 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)) i (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)))
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (LocalEquiv.toFun.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u1} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u3, u2, u1} ι B F _inst_2 _inst_3 Z i) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (FiberBundleCore.coordChange.{u3, u2, u1} ι B _inst_2 F _inst_3 Z (FiberBundleCore.indexAt.{u3, u2, u1} ι B _inst_2 F _inst_3 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p)) i (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_applyₓ'. -/
 theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
     (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
@@ -606,9 +656,9 @@ theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
 
 /- warning: fiber_bundle_core.local_triv_as_local_equiv_trans -> FiberBundleCore.localTrivAsLocalEquiv_trans is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (j : ι), HasEquivₓ.Equiv.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F)) (setoidHasEquiv.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F)) (LocalEquiv.eqOnSourceSetoid.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F))) (LocalEquiv.trans.{max u2 u3, max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z j)) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i j))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (j : ι), HasEquivₓ.Equiv.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F)) (setoidHasEquiv.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F)) (LocalEquiv.eqOnSourceSetoid.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F))) (LocalEquiv.trans.{max u2 u3, max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z j)) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (FiberBundleCore.trivChange.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i j))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (j : ι), HasEquiv.Equiv.{max (max (succ u3) (succ u2)) (succ (max u3 u2)), 0} (LocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F)) (instHasEquiv.{max (succ u3) (succ u2)} (LocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F)) (LocalEquiv.eqOnSourceSetoid.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F))) (LocalEquiv.trans.{max u3 u2, max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (LocalEquiv.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z j)) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i j))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι) (j : ι), HasEquiv.Equiv.{max (max (succ u3) (succ u2)) (succ (max u3 u2)), 0} (LocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F)) (instHasEquiv.{max (succ u3) (succ u2)} (LocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F)) (LocalEquiv.eqOnSourceSetoid.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F))) (LocalEquiv.trans.{max u3 u2, max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (LocalEquiv.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z j)) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (FiberBundleCore.trivChange.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i j))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_transₓ'. -/
 /-- The composition of two local trivializations is the trivialization change Z.triv_change i j. -/
 theorem localTrivAsLocalEquiv_trans (i j : ι) :
@@ -640,9 +690,9 @@ variable (b : B) (a : F)
 
 /- warning: fiber_bundle_core.open_source' -> FiberBundleCore.open_source' is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι), IsOpen.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι), IsOpen.{max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι), IsOpen.{max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.open_source' FiberBundleCore.open_source'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
@@ -714,9 +764,9 @@ def localTrivAt (b : B) : Trivialization F (π Z.Fiber) :=
 
 /- warning: fiber_bundle_core.local_triv_at_def -> FiberBundleCore.localTrivAt_def is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (b : B), Eq.{max (succ u2) (succ u3) (succ (max u2 u3))} (Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_2 F _inst_3 Z b)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b)
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (b : B), Eq.{max (succ u3) (succ u2)} (Trivialization.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z (FiberBundleCore.indexAt.{u1, u3, u2} ι B _inst_1 F _inst_2 Z b)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b)
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (b : B), Eq.{max (succ u3) (succ u2)} (Trivialization.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z (FiberBundleCore.indexAt.{u1, u3, u2} ι B _inst_2 F _inst_3 Z b)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_at_def FiberBundleCore.localTrivAt_defₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAt_def (b : B) : Z.localTriv (Z.indexAt b) = Z.localTrivAt b :=
@@ -725,9 +775,9 @@ theorem localTrivAt_def (b : B) : Z.localTriv (Z.indexAt b) = Z.localTrivAt b :=
 
 /- warning: fiber_bundle_core.continuous_const_section -> FiberBundleCore.continuous_const_section is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (v : F), (forall (i : ι) (j : ι) (x : B), (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) x (Inter.inter.{u2} (Set.{u2} B) (Set.hasInter.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z j))) -> (Eq.{succ u3} F (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i j x v) v)) -> (Continuous.{u2, max u2 u3} B (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) ((fun (this : B -> (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) => this) (fun (x : B) => Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) x v)))
 but is expected to have type
-  forall {ι : Type.{u2}} {B : Type.{u3}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u2, u3, u1} ι B _inst_1 F _inst_2) (v : F), (forall (i : ι) (j : ι) (x : B), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_1 F _inst_2 Z i) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_1 F _inst_2 Z j))) -> (Eq.{succ u1} F (FiberBundleCore.coordChange.{u2, u3, u1} ι B _inst_1 F _inst_2 Z i j x v) v)) -> (Continuous.{u3, max u3 u1} B (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.toTopologicalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) ([mdata let_fun:1 (fun (this : B -> (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z)) => this) (fun (x : B) => Sigma.mk.{u3, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u2, u3, u1} ι B F _inst_1 _inst_2 Z x) x v)]))
+  forall {ι : Type.{u2}} {B : Type.{u3}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u2, u3, u1} ι B _inst_2 F _inst_3) (v : F), (forall (i : ι) (j : ι) (x : B), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_2 F _inst_3 Z i) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_2 F _inst_3 Z j))) -> (Eq.{succ u1} F (FiberBundleCore.coordChange.{u2, u3, u1} ι B _inst_2 F _inst_3 Z i j x v) v)) -> (Continuous.{u3, max u3 u1} B (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_2 _inst_3 Z) _inst_2 (FiberBundleCore.toTopologicalSpace.{u2, u3, u1} ι B F _inst_2 _inst_3 Z) ([mdata let_fun:1 (fun (this : B -> (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_2 _inst_3 Z)) => this) (fun (x : B) => Sigma.mk.{u3, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u2, u3, u1} ι B F _inst_2 _inst_3 Z x) x v)]))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.continuous_const_section FiberBundleCore.continuous_const_sectionₓ'. -/
 /-- If an element of `F` is invariant under all coordinate changes, then one can define a
 corresponding section of the fiber bundle, which is continuous. This applies in particular to the
@@ -752,9 +802,9 @@ theorem continuous_const_section (v : F)
 
 /- warning: fiber_bundle_core.local_triv_as_local_equiv_coe -> FiberBundleCore.localTrivAsLocalEquiv_coe is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ (max u2 u3)} ((FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) -> (Prod.{u2, u3} B F)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F)) (fun (_x : LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) -> (Prod.{u2, u3} B F)) (LocalEquiv.hasCoeToFun.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)) (coeFn.{max (succ u2) (succ u3) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u2) (succ u3)} (Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (fun (_x : Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) -> (Prod.{u2, u3} B F)) (Trivialization.hasCoeToFun.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι), Eq.{succ (max u2 u3)} ((FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) -> (Prod.{u2, u3} B F)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F)) (fun (_x : LocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) -> (Prod.{u2, u3} B F)) (LocalEquiv.hasCoeToFun.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)) (coeFn.{max (succ u2) (succ u3) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u2) (succ u3)} (Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (fun (_x : Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) -> (Prod.{u2, u3} B F)) (Trivialization.hasCoeToFun.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι), Eq.{max (succ u3) (succ u2)} ((FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) -> (Prod.{u3, u2} B F)) (LocalEquiv.toFun.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)) (Trivialization.toFun'.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι), Eq.{max (succ u3) (succ u2)} ((FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) -> (Prod.{u3, u2} B F)) (LocalEquiv.toFun.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i)) (Trivialization.toFun'.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsLocalEquiv_coeₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv i :=
@@ -763,9 +813,9 @@ theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv
 
 /- warning: fiber_bundle_core.local_triv_as_local_equiv_source -> FiberBundleCore.localTrivAsLocalEquiv_source is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)) (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)) (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i)) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsLocalEquiv_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_source :
@@ -775,9 +825,9 @@ theorem localTrivAsLocalEquiv_source :
 
 /- warning: fiber_bundle_core.local_triv_as_local_equiv_target -> FiberBundleCore.localTrivAsLocalEquiv_target is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} B F)) (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)) (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)) (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i)) (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsLocalEquiv_targetₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_target :
@@ -787,9 +837,9 @@ theorem localTrivAsLocalEquiv_target :
 
 /- warning: fiber_bundle_core.local_triv_as_local_equiv_symm -> FiberBundleCore.localTrivAsLocalEquiv_symm is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι), Eq.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι), Eq.{max (succ u3) (succ u2)} (LocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (LocalEquiv.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)) (LocalEquiv.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι), Eq.{max (succ u3) (succ u2)} (LocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (LocalEquiv.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i)) (LocalEquiv.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsLocalEquiv_symmₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_symm :
@@ -799,9 +849,9 @@ theorem localTrivAsLocalEquiv_symm :
 
 /- warning: fiber_bundle_core.base_set_at -> FiberBundleCore.baseSet_at is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ u2} (Set.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι), Eq.{succ u2} (Set.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))
 but is expected to have type
-  forall {ι : Type.{u2}} {B : Type.{u3}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u2, u3, u1} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ u3} (Set.{u3} B) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_1 F _inst_2 Z i) (Trivialization.baseSet.{u3, u1, max u3 u1} B F (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u2, u3, u1} ι B F _inst_1 _inst_2 Z i))
+  forall {ι : Type.{u2}} {B : Type.{u3}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u2, u3, u1} ι B _inst_2 F _inst_3) (i : ι), Eq.{succ u3} (Set.{u3} B) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_2 F _inst_3 Z i) (Trivialization.baseSet.{u3, u1, max u3 u1} B F (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u2, u3, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u2, u3, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u2, u3, u1} ι B F _inst_2 _inst_3 Z i))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.base_set_at FiberBundleCore.baseSet_atₓ'. -/
 @[simp, mfld_simps]
 theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
@@ -810,9 +860,9 @@ theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
 
 /- warning: fiber_bundle_core.local_triv_apply -> FiberBundleCore.localTriv_apply is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} B F) (coeFn.{max (succ u2) (succ u3) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u2) (succ u3)} (Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (fun (_x : Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) -> (Prod.{u2, u3} B F)) (Trivialization.hasCoeToFun.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i) p) (Prod.mk.{u2, u3} B F (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_1 F _inst_2 Z (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_1 F _inst_2 Z (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p)) i (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (Sigma.snd.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} B F) (coeFn.{max (succ u2) (succ u3) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u2) (succ u3)} (Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (fun (_x : Trivialization.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) => (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) -> (Prod.{u2, u3} B F)) (Trivialization.hasCoeToFun.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i) p) (Prod.mk.{u2, u3} B F (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_2 F _inst_3 Z (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_2 F _inst_3 Z (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p)) i (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p)))
 but is expected to have type
-  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (Trivialization.toFun'.{u2, u1, max u2 u1} B F (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.proj.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.coordChange.{u3, u2, u1} ι B _inst_1 F _inst_2 Z (FiberBundleCore.indexAt.{u3, u2, u1} ι B _inst_1 F _inst_2 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)) i (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)))
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (Trivialization.toFun'.{u2, u1, max u2 u1} B F (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.proj.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u3, u2, u1} ι B F _inst_2 _inst_3 Z i) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (FiberBundleCore.coordChange.{u3, u2, u1} ι B _inst_2 F _inst_3 Z (FiberBundleCore.indexAt.{u3, u2, u1} ι B _inst_2 F _inst_3 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p)) i (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_applyₓ'. -/
 @[simp, mfld_simps]
 theorem localTriv_apply (p : Z.TotalSpace) :
@@ -822,9 +872,9 @@ theorem localTriv_apply (p : Z.TotalSpace) :
 
 /- warning: fiber_bundle_core.local_triv_at_apply -> FiberBundleCore.localTrivAt_apply is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} B F) (coeFn.{max (succ u2) (succ u3) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u2) (succ u3)} (Trivialization.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) (fun (_x : Trivialization.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) => (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) -> (Prod.{u2, u3} B F)) (Trivialization.hasCoeToFun.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p)) p) (Prod.mk.{u2, u3} B F (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p))
 but is expected to have type
-  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (Trivialization.toFun'.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_1 _inst_2 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p))
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (Trivialization.toFun'.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_2 _inst_3 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p)) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_applyₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ :=
@@ -835,9 +885,9 @@ theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p
 
 /- warning: fiber_bundle_core.local_triv_at_apply_mk -> FiberBundleCore.localTrivAt_apply_mk is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (b : B) (a : F), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} B F) (coeFn.{max (succ u2) (succ u3) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u2) (succ u3)} (Trivialization.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) (fun (_x : Trivialization.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) => (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) -> (Prod.{u2, u3} B F)) (Trivialization.hasCoeToFun.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) b a)) (Prod.mk.{u2, u3} B F b a)
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (b : B) (a : F), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} B F) (Trivialization.toFun'.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x) b a)) (Prod.mk.{u3, u2} B F b a)
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (b : B) (a : F), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} B F) (Trivialization.toFun'.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z x) b a)) (Prod.mk.{u3, u2} B F b a)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_at_apply_mk FiberBundleCore.localTrivAt_apply_mkₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = ⟨b, a⟩ :=
@@ -846,9 +896,9 @@ theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = 
 
 /- warning: fiber_bundle_core.mem_local_triv_source -> FiberBundleCore.mem_localTriv_source is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Set.hasMem.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Set.hasMem.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)))
 but is expected to have type
-  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Set.instMembershipSet.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) p (LocalEquiv.source.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u1} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u1} B F) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u2, u1} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u1, max u2 u1} B F (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i))))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Trivialization.baseSet.{u2, u1, max u2 u1} B F (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i)))
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Set.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (Set.instMembershipSet.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) p (LocalEquiv.source.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u1} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u1} B F) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u2, u1} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u1, max u2 u1} B F (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u3, u2, u1} ι B F _inst_2 _inst_3 Z i))))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (Trivialization.baseSet.{u2, u1, max u2 u1} B F (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u3, u2, u1} ι B F _inst_2 _inst_3 Z i)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTriv_source (p : Z.TotalSpace) :
@@ -858,9 +908,9 @@ theorem mem_localTriv_source (p : Z.TotalSpace) :
 
 /- warning: fiber_bundle_core.mem_local_triv_at_source -> FiberBundleCore.mem_localTrivAt_source is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (b : B), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) (Set.hasMem.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) p (LocalEquiv.source.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (b : B), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) (Set.hasMem.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) p (LocalEquiv.source.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b)))
 but is expected to have type
-  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (b : B), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z))) (Set.instMembershipSet.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z))) p (LocalEquiv.source.{max u2 u1, max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u1} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u1, max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u1} B F) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u2, u1} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_1 _inst_2 Z b))))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Trivialization.baseSet.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_1 _inst_2 Z b)))
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_2 F _inst_3) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (b : B), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Set.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z))) (Set.instMembershipSet.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z))) p (LocalEquiv.source.{max u2 u1, max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u1} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u1, max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u1} B F) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u2, u1} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_2 _inst_3 Z b))))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z x) p) (Trivialization.baseSet.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_2 _inst_3 Z b)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
@@ -870,9 +920,9 @@ theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
 
 /- warning: fiber_bundle_core.mem_source_at -> FiberBundleCore.mem_source_at is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (b : B) (a : F), Membership.Mem.{max u2 u3, max u2 u3} (Sigma.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x)) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) (Set.hasMem.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) b a) (LocalEquiv.source.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (b : B) (a : F), Membership.Mem.{max u2 u3, max u2 u3} (Sigma.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x)) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) (Set.hasMem.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z))) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) b a) (LocalEquiv.source.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b))))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (b : B) (a : F), Membership.mem.{max u3 u2, max u3 u2} (Sigma.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x)) (Set.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z))) (Set.instMembershipSet.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z))) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x) b a) (LocalEquiv.source.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b))))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (b : B) (a : F), Membership.mem.{max u3 u2, max u3 u2} (Sigma.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z x)) (Set.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z))) (Set.instMembershipSet.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z))) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z x) b a) (LocalEquiv.source.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b))))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_atₓ'. -/
 @[simp, mfld_simps]
 theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source :=
@@ -883,9 +933,9 @@ theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source
 
 /- warning: fiber_bundle_core.mem_local_triv_target -> FiberBundleCore.mem_localTriv_target is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i)))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Trivialization.baseSet.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Trivialization.baseSet.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_target FiberBundleCore.mem_localTriv_targetₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTriv_target (p : B × F) :
@@ -895,9 +945,9 @@ theorem mem_localTriv_target (p : B × F) :
 
 /- warning: fiber_bundle_core.mem_local_triv_at_target -> FiberBundleCore.mem_localTrivAt_target is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (p : Prod.{u2, u3} B F) (b : B), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (p : Prod.{u2, u3} B F) (b : B), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b)))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (p : Prod.{u3, u2} B F) (b : B), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b))))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b)))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (p : Prod.{u3, u2} B F) (b : B), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b))))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_target FiberBundleCore.mem_localTrivAt_targetₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTrivAt_target (p : B × F) (b : B) :
@@ -907,9 +957,9 @@ theorem mem_localTrivAt_target (p : B × F) (b : B) :
 
 /- warning: fiber_bundle_core.local_triv_symm_apply -> FiberBundleCore.localTriv_symm_apply is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u2, u3} B F), Eq.{max (succ u2) (succ u3)} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (fun (_x : LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) => (Prod.{u2, u3} B F) -> (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (LocalHomeomorph.hasCoeToFun.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (LocalHomeomorph.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))) p) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) (Prod.fst.{u2, u3} B F p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_1 F _inst_2 Z (Prod.fst.{u2, u3} B F p)) (Prod.fst.{u2, u3} B F p) (Prod.snd.{u2, u3} B F p)))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u2, u3} B F), Eq.{max (succ u2) (succ u3)} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (fun (_x : LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) => (Prod.{u2, u3} B F) -> (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (LocalHomeomorph.hasCoeToFun.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (LocalHomeomorph.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_2 _inst_3 Z i))) p) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z x) (Prod.fst.{u2, u3} B F p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_2 F _inst_3 Z i (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_2 F _inst_3 Z (Prod.fst.{u2, u3} B F p)) (Prod.fst.{u2, u3} B F p) (Prod.snd.{u2, u3} B F p)))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u3, u2} B F), Eq.{max (succ u3) (succ u2)} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (LocalHomeomorph.toFun'.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (LocalHomeomorph.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))) p) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.coordChange.{u1, u3, u2} ι B _inst_1 F _inst_2 Z i (FiberBundleCore.indexAt.{u1, u3, u2} ι B _inst_1 F _inst_2 Z (Prod.fst.{u3, u2} B F p)) (Prod.fst.{u3, u2} B F p) (Prod.snd.{u3, u2} B F p)))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (i : ι) (p : Prod.{u3, u2} B F), Eq.{max (succ u3) (succ u2)} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (LocalHomeomorph.toFun'.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (LocalHomeomorph.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_2 _inst_3 Z i))) p) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z x) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.coordChange.{u1, u3, u2} ι B _inst_2 F _inst_3 Z i (FiberBundleCore.indexAt.{u1, u3, u2} ι B _inst_2 F _inst_3 Z (Prod.fst.{u3, u2} B F p)) (Prod.fst.{u3, u2} B F p) (Prod.snd.{u3, u2} B F p)))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_applyₓ'. -/
 @[simp, mfld_simps]
 theorem localTriv_symm_apply (p : B × F) :
@@ -919,9 +969,9 @@ theorem localTriv_symm_apply (p : B × F) :
 
 /- warning: fiber_bundle_core.mem_local_triv_at_base_set -> FiberBundleCore.mem_localTrivAt_baseSet is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (b : B), Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) b (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3) (b : B), Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) b (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_2 _inst_3 Z b))
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (b : B), Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b))
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3) (b : B), Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) _inst_2 _inst_3 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_2 _inst_3 Z b))
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSetₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet :=
@@ -995,9 +1045,9 @@ instance fiberBundle : FiberBundle F Z.Fiber
 
 /- warning: fiber_bundle_core.continuous_proj -> FiberBundleCore.continuous_proj is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2), Continuous.{max u2 u3, u2} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3), Continuous.{max u2 u3, u2} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2), Continuous.{max u3 u2, u3} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3), Continuous.{max u3 u2, u3} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.continuous_proj FiberBundleCore.continuous_projₓ'. -/
 /-- The projection on the base of a fiber bundle created from core is continuous -/
 theorem continuous_proj : Continuous Z.proj :=
@@ -1006,9 +1056,9 @@ theorem continuous_proj : Continuous Z.proj :=
 
 /- warning: fiber_bundle_core.is_open_map_proj -> FiberBundleCore.isOpenMap_proj is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2), IsOpenMap.{max u2 u3, u2} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_2 F _inst_3), IsOpenMap.{max u2 u3, u2} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_2 _inst_3 Z) _inst_2 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_2 _inst_3 Z)
 but is expected to have type
-  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2), IsOpenMap.{max u3 u2, u3} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_2 F _inst_3), IsOpenMap.{max u3 u2, u3} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_2 _inst_3 Z) _inst_2 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_2 _inst_3 Z)
 Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.is_open_map_proj FiberBundleCore.isOpenMap_projₓ'. -/
 /-- The projection on the base of a fiber bundle created from core is an open map -/
 theorem isOpenMap_proj : IsOpenMap Z.proj :=
@@ -1054,9 +1104,9 @@ def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E
 
 /- warning: fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas -> FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) {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.{max u1 u2 u1 u3, max u1 u2 u1 u3} (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)) (Set.{max u1 u2 u1 u3} (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))) (Set.hasMem.{max u1 u2 u1 u3} (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))) e (FiberPrebundle.pretrivializationAtlas.{u1, u2, u3} B F E _inst_1 _inst_2 a)) -> (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) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (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))) (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)))
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) {e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)}, (Membership.Mem.{max u1 u2 u1 u3, max u1 u2 u1 u3} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) (Set.{max u1 u2 u1 u3} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E))) (Set.hasMem.{max u1 u2 u1 u3} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E))) e (FiberPrebundle.pretrivializationAtlas.{u1, u2, u3} B F E _inst_2 _inst_3 a)) -> (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_2 _inst_3) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a) (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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e))) (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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e)))
 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] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_1 _inst_2) {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.{max (max u3 u2) u1, max (max u3 u2) u1} (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)) (Set.{max (max (max u3 u1) u2) u3} (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))) (Set.instMembershipSet.{max (max u3 u2) u1} (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))) e (FiberPrebundle.pretrivializationAtlas.{u3, u2, u1} B F E _inst_1 _inst_2 a)) -> (ContinuousOn.{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) (FiberPrebundle.totalSpaceTopology.{u3, u2, u1} B F E _inst_1 _inst_2 a) (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))) (LocalEquiv.target.{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)))
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_2 _inst_3) {e : Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)}, (Membership.mem.{max (max u3 u2) u1, max (max u3 u2) u1} (Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) (Set.{max (max (max u3 u1) u2) u3} (Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E))) (Set.instMembershipSet.{max (max u3 u2) u1} (Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E))) e (FiberPrebundle.pretrivializationAtlas.{u3, u2, u1} B F E _inst_2 _inst_3 a)) -> (ContinuousOn.{max u3 u2, max u3 u1} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (FiberPrebundle.totalSpaceTopology.{u3, u2, u1} B F E _inst_2 _inst_3 a) (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_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e))) (LocalEquiv.target.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e)))
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlasₓ'. -/
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
@@ -1069,9 +1119,9 @@ theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializ
 
 /- warning: fiber_prebundle.is_open_source -> FiberPrebundle.isOpen_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (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)), IsOpen.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (LocalEquiv.source.{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))
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)), IsOpen.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a) (LocalEquiv.source.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e))
 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] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_1 _inst_2) (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)), IsOpen.{max u3 u1} (Bundle.TotalSpace.{u3, u1} B E) (FiberPrebundle.totalSpaceTopology.{u3, u2, u1} B F E _inst_1 _inst_2 a) (LocalEquiv.source.{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))
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_2 _inst_3) (e : Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)), IsOpen.{max u3 u1} (Bundle.TotalSpace.{u3, u1} B E) (FiberPrebundle.totalSpaceTopology.{u3, u2, u1} B F E _inst_2 _inst_3 a) (LocalEquiv.source.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e))
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.is_open_source FiberPrebundle.isOpen_sourceₓ'. -/
 theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTopology] e.source :=
   by
@@ -1086,9 +1136,9 @@ theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTop
 
 /- warning: fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter -> FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (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)) (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.{max u1 u2 u1 u3, max u1 u2 u1 u3} (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)) (Set.{max u1 u2 u1 u3} (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))) (Set.hasMem.{max u1 u2 u1 u3} (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))) e' (FiberPrebundle.pretrivializationAtlas.{u1, u2, u3} B F E _inst_1 _inst_2 a)) -> (IsOpen.{max u1 u2} (Prod.{u1, u2} B F) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Inter.inter.{max u1 u2} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (Set.hasInter.{max u1 u2} (Prod.{u1, u2} B F)) (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')) (Set.preimage.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (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'))) (LocalEquiv.source.{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)))))
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) (e : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) (e' : Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)), (Membership.Mem.{max u1 u2 u1 u3, max u1 u2 u1 u3} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) (Set.{max u1 u2 u1 u3} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E))) (Set.hasMem.{max u1 u2 u1 u3} (Pretrivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E))) e' (FiberPrebundle.pretrivializationAtlas.{u1, u2, u3} B F E _inst_2 _inst_3 a)) -> (IsOpen.{max u1 u2} (Prod.{u1, u2} B F) (Prod.topologicalSpace.{u1, u2} B F _inst_2 _inst_3) (Inter.inter.{max u1 u2} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (Set.hasInter.{max u1 u2} (Prod.{u1, u2} B F)) (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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e')) (Set.preimage.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e'))) (LocalEquiv.source.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e)))))
 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] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_1 _inst_2) (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)) (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.{max (max u3 u2) u1, max (max u3 u2) u1} (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)) (Set.{max (max (max u3 u1) u2) u3} (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))) (Set.instMembershipSet.{max (max u3 u2) u1} (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))) e' (FiberPrebundle.pretrivializationAtlas.{u3, u2, u1} B F E _inst_1 _inst_2 a)) -> (IsOpen.{max u3 u2} (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Inter.inter.{max u3 u2} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instInterSet.{max u3 u2} (Prod.{u3, u2} B F)) (LocalEquiv.target.{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')) (Set.preimage.{max u3 u2, max u3 u1} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (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'))) (LocalEquiv.source.{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)))))
+  forall {B : Type.{u3}} {F : Type.{u2}} {E : B -> Type.{u1}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_2 _inst_3) (e : Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) (e' : Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)), (Membership.mem.{max (max u3 u2) u1, max (max u3 u2) u1} (Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) (Set.{max (max (max u3 u1) u2) u3} (Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E))) (Set.instMembershipSet.{max (max u3 u2) u1} (Pretrivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E))) e' (FiberPrebundle.pretrivializationAtlas.{u3, u2, u1} B F E _inst_2 _inst_3 a)) -> (IsOpen.{max u3 u2} (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_2 _inst_3) (Inter.inter.{max u3 u2} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instInterSet.{max u3 u2} (Prod.{u3, u2} B F)) (LocalEquiv.target.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e')) (Set.preimage.{max u3 u2, max u3 u1} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (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_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e'))) (LocalEquiv.source.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e)))))
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_interₓ'. -/
 theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π E))
     (he' : e' ∈ a.pretrivializationAtlas) :
@@ -1134,9 +1184,9 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
 
 /- warning: fiber_prebundle.mem_trivialization_at_source -> FiberPrebundle.mem_pretrivializationAt_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B) (x : E b), Membership.Mem.{max u1 u3, max u1 u3} (Bundle.TotalSpace.{u1, u3} B (fun (b : B) => E b)) (Set.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Set.hasMem.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Bundle.totalSpaceMk.{u1, u3} B (fun (b : B) => E b) b x) (LocalEquiv.source.{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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b)))
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) (b : B) (x : E b), Membership.Mem.{max u1 u3, max u1 u3} (Bundle.TotalSpace.{u1, u3} B (fun (b : B) => E b)) (Set.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Set.hasMem.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Bundle.totalSpaceMk.{u1, u3} B (fun (b : B) => E b) b x) (LocalEquiv.source.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_2 _inst_3 a b)))
 but is expected to have type
-  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B) (x : E b), Membership.mem.{max u3 u2, max u2 u3} (Bundle.TotalSpace.{u2, u3} B E) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B E)) (Set.instMembershipSet.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B E)) (Bundle.totalSpaceMk.{u2, u3} B E b x) (LocalEquiv.source.{max u2 u3, max u2 u1} (Bundle.TotalSpace.{u2, u3} B E) (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u3} B E) (FiberPrebundle.pretrivializationAt.{u2, u1, u3} B F E _inst_1 _inst_2 a b)))
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_2 _inst_3) (b : B) (x : E b), Membership.mem.{max u3 u2, max u2 u3} (Bundle.TotalSpace.{u2, u3} B E) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B E)) (Set.instMembershipSet.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B E)) (Bundle.totalSpaceMk.{u2, u3} B E b x) (LocalEquiv.source.{max u2 u3, max u2 u1} (Bundle.TotalSpace.{u2, u3} B E) (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u2, u3} B E) (FiberPrebundle.pretrivializationAt.{u2, u1, u3} B F E _inst_2 _inst_3 a b)))
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_pretrivializationAt_sourceₓ'. -/
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
     totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
@@ -1147,9 +1197,9 @@ theorem mem_pretrivializationAt_source (b : B) (x : E b) :
 
 /- warning: fiber_prebundle.total_space_mk_preimage_source -> FiberPrebundle.totalSpaceMk_preimage_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B), Eq.{succ u3} (Set.{u3} (E b)) (Set.preimage.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (Bundle.totalSpaceMk.{u1, u3} B E b) (LocalEquiv.source.{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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b)))) (Set.univ.{u3} (E b))
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) (b : B), Eq.{succ u3} (Set.{u3} (E b)) (Set.preimage.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (Bundle.totalSpaceMk.{u1, u3} B E b) (LocalEquiv.source.{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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_2 _inst_3 a b)))) (Set.univ.{u3} (E b))
 but is expected to have type
-  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B), Eq.{succ u3} (Set.{u3} (E b)) (Set.preimage.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (Bundle.totalSpaceMk.{u2, u3} B E b) (LocalEquiv.source.{max u2 u3, max u2 u1} (Bundle.TotalSpace.{u2, u3} B E) (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u3} B E) (FiberPrebundle.pretrivializationAt.{u2, u1, u3} B F E _inst_1 _inst_2 a b)))) (Set.univ.{u3} (E b))
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_2 _inst_3) (b : B), Eq.{succ u3} (Set.{u3} (E b)) (Set.preimage.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (Bundle.totalSpaceMk.{u2, u3} B E b) (LocalEquiv.source.{max u2 u3, max u2 u1} (Bundle.TotalSpace.{u2, u3} B E) (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u2, u3} B E) (FiberPrebundle.pretrivializationAt.{u2, u1, u3} B F E _inst_2 _inst_3 a b)))) (Set.univ.{u3} (E b))
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_sourceₓ'. -/
 @[simp]
 theorem totalSpaceMk_preimage_source (b : B) :
@@ -1171,9 +1221,9 @@ def fiberTopology (b : B) : TopologicalSpace (E b) :=
 
 /- warning: fiber_prebundle.inducing_total_space_mk -> FiberPrebundle.inducing_totalSpaceMk 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B), Inducing.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.fiberTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u1, u3} B E b)
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) (b : B), Inducing.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.fiberTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a b) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a) (Bundle.totalSpaceMk.{u1, u3} B E b)
 but is expected to have type
-  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B), Inducing.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (FiberPrebundle.fiberTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u2, u3} B E b)
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_2 _inst_3) (b : B), Inducing.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (FiberPrebundle.fiberTopology.{u2, u1, u3} B F E _inst_2 _inst_3 a b) (FiberPrebundle.totalSpaceTopology.{u2, u1, u3} B F E _inst_2 _inst_3 a) (Bundle.totalSpaceMk.{u2, u3} B E b)
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMkₓ'. -/
 @[continuity]
 theorem inducing_totalSpaceMk (b : B) :
@@ -1186,9 +1236,9 @@ theorem inducing_totalSpaceMk (b : B) :
 
 /- warning: fiber_prebundle.continuous_total_space_mk -> FiberPrebundle.continuous_totalSpaceMk 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B), Continuous.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.fiberTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u1, u3} B E b)
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) (b : B), Continuous.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.fiberTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a b) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a) (Bundle.totalSpaceMk.{u1, u3} B E b)
 but is expected to have type
-  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B), Continuous.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (FiberPrebundle.fiberTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u2, u3} B E b)
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u2} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_2 _inst_3) (b : B), Continuous.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (FiberPrebundle.fiberTopology.{u2, u1, u3} B F E _inst_2 _inst_3 a b) (FiberPrebundle.totalSpaceTopology.{u2, u1, u3} B F E _inst_2 _inst_3 a) (Bundle.totalSpaceMk.{u2, u3} B E b)
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMkₓ'. -/
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
@@ -1221,9 +1271,9 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology
 
 /- warning: fiber_prebundle.continuous_proj -> FiberPrebundle.continuous_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2), Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3), Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a) _inst_2 (Bundle.TotalSpace.proj.{u1, u3} B E)
 but is expected to have type
-  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_1 _inst_2), Continuous.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_1 _inst_2 a) _inst_1 (Bundle.TotalSpace.proj.{u3, u2} B E)
+  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_2 _inst_3), Continuous.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_2 _inst_3 a) _inst_2 (Bundle.TotalSpace.proj.{u3, u2} B E)
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_proj FiberPrebundle.continuous_projₓ'. -/
 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   by
@@ -1235,9 +1285,9 @@ theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
 
 /- warning: fiber_prebundle.continuous_on_of_comp_right -> FiberPrebundle.continuousOn_of_comp_right 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) {X : Type.{u4}} [_inst_3 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u1, u3} B E) -> X} {s : Set.{u1} B}, (IsOpen.{u1} B _inst_1 s) -> (forall (b : B), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b s) -> (ContinuousOn.{max u1 u2, u4} (Prod.{u1, u2} B F) X (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_3 (Function.comp.{succ (max u1 u2), max (succ u1) (succ u3), succ u4} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) X f (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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b))))) (Set.prod.{u1, u2} B F (Inter.inter.{u1} (Set.{u1} B) (Set.hasInter.{u1} B) s (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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b))) (Set.univ.{u2} F)))) -> (ContinuousOn.{max u1 u3, u4} (Bundle.TotalSpace.{u1, u3} B E) X (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) _inst_3 f (Set.preimage.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) s))
+  forall {B : Type.{u1}} {F : Type.{u2}} {E : B -> Type.{u3}} [_inst_2 : TopologicalSpace.{u1} B] [_inst_3 : TopologicalSpace.{u2} F] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_2 _inst_3) {X : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u1, u3} B E) -> X} {s : Set.{u1} B}, (IsOpen.{u1} B _inst_2 s) -> (forall (b : B), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b s) -> (ContinuousOn.{max u1 u2, u4} (Prod.{u1, u2} B F) X (Prod.topologicalSpace.{u1, u2} B F _inst_2 _inst_3) _inst_4 (Function.comp.{succ (max u1 u2), max (succ u1) (succ u3), succ u4} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) X f (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_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_2 _inst_3 a b))))) (Set.prod.{u1, u2} B F (Inter.inter.{u1} (Set.{u1} B) (Set.hasInter.{u1} B) s (Pretrivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_2 _inst_3 a b))) (Set.univ.{u2} F)))) -> (ContinuousOn.{max u1 u3, u4} (Bundle.TotalSpace.{u1, u3} B E) X (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_2 _inst_3 a) _inst_4 f (Set.preimage.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) s))
 but is expected to have type
-  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_1 _inst_2) {X : Type.{u4}} [_inst_3 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u3, u2} B E) -> X} {s : Set.{u3} B}, (IsOpen.{u3} B _inst_1 s) -> (forall (b : B), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b s) -> (ContinuousOn.{max u3 u1, u4} (Prod.{u3, u1} B F) X (instTopologicalSpaceProd.{u3, u1} B F _inst_1 _inst_2) _inst_3 (Function.comp.{succ (max u3 u1), max (succ u3) (succ u2), succ u4} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) X f (LocalEquiv.toFun.{max u3 u1, max u3 u2} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) (LocalEquiv.symm.{max u3 u2, max u3 u1} (Bundle.TotalSpace.{u3, u2} B E) (Prod.{u3, u1} B F) (Pretrivialization.toLocalEquiv.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_1 _inst_2 a b))))) (Set.prod.{u3, u1} B F (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) s (Pretrivialization.baseSet.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_1 _inst_2 a b))) (Set.univ.{u1} F)))) -> (ContinuousOn.{max u3 u2, u4} (Bundle.TotalSpace.{u3, u2} B E) X (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_1 _inst_2 a) _inst_3 f (Set.preimage.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (Bundle.TotalSpace.proj.{u3, u2} B E) s))
+  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_2 : TopologicalSpace.{u3} B] [_inst_3 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_2 _inst_3) {X : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u3, u2} B E) -> X} {s : Set.{u3} B}, (IsOpen.{u3} B _inst_2 s) -> (forall (b : B), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b s) -> (ContinuousOn.{max u3 u1, u4} (Prod.{u3, u1} B F) X (instTopologicalSpaceProd.{u3, u1} B F _inst_2 _inst_3) _inst_4 (Function.comp.{succ (max u3 u1), max (succ u3) (succ u2), succ u4} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) X f (LocalEquiv.toFun.{max u3 u1, max u3 u2} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) (LocalEquiv.symm.{max u3 u2, max u3 u1} (Bundle.TotalSpace.{u3, u2} B E) (Prod.{u3, u1} B F) (Pretrivialization.toLocalEquiv.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_2 _inst_3 a b))))) (Set.prod.{u3, u1} B F (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) s (Pretrivialization.baseSet.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_2 _inst_3 a b))) (Set.univ.{u1} F)))) -> (ContinuousOn.{max u3 u2, u4} (Bundle.TotalSpace.{u3, u2} B E) X (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_2 _inst_3 a) _inst_4 f (Set.preimage.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (Bundle.TotalSpace.proj.{u3, u2} B E) s))
 Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_on_of_comp_right FiberPrebundle.continuousOn_of_comp_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- For a fiber bundle `E` over `B` constructed using the `fiber_prebundle` mechanism,

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit 8ef6f08ff8c781c5c07a8b12843710e1a0d8a688
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.FiberBundle.Trivialization
 /-!
 # Fiber bundles
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Mathematically, a (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on
 `B` for which the fibers are all homeomorphic to `F`, such that the local situation around each
 point is a direct product.

mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8

@@ -187,6 +187,7 @@ section FiberBundle
 variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
   [TopologicalSpace (TotalSpace E)] [∀ b, TopologicalSpace (E b)]
 
+#print FiberBundle /-
 /- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`totalSpaceMk_inducing] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`trivializationAtlas] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`trivializationAt] [] -/
@@ -202,11 +203,13 @@ class FiberBundle where
   mem_baseSet_trivializationAt : ∀ b : B, b ∈ (trivialization_at b).baseSet
   trivialization_mem_atlas : ∀ b : B, trivialization_at b ∈ trivialization_atlas
 #align fiber_bundle FiberBundle
+-/
 
 export FiberBundle ()
 
 variable {F E}
 
+#print MemTrivializationAtlas /-
 /-- Given a type `E` equipped with a fiber bundle structure, this is a `Prop` typeclass
 for trivializations of `E`, expressing that a trivialization is in the designated atlas for the
 bundle.  This is needed because lemmas about the linearity of trivializations or the continuity (as
@@ -216,6 +219,7 @@ expected to hold for trivializations in the designated atlas. -/
 class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π E)) : Prop where
   out : e ∈ trivializationAtlas F E
 #align mem_trivialization_atlas MemTrivializationAtlas
+-/
 
 instance [FiberBundle F E] (b : B) : MemTrivializationAtlas (trivializationAt F E b)
     where out := trivialization_mem_atlas F E b
@@ -224,6 +228,12 @@ namespace FiberBundle
 
 variable (F) {E} [FiberBundle F E]
 
+/- warning: fiber_bundle.map_proj_nhds -> FiberBundle.map_proj_nhds is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] {E : B -> Type.{u3}} [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : Bundle.TotalSpace.{u1, u3} B E), Eq.{succ u1} (Filter.{u1} B) (Filter.map.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) (nhds.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) _inst_3 x)) (nhds.{u1} B _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E x))
+but is expected to have type
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] {E : B -> Type.{u1}} [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : Bundle.TotalSpace.{u2, u1} B E), Eq.{succ u2} (Filter.{u2} B) (Filter.map.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E) (nhds.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B E) _inst_3 x)) (nhds.{u2} B _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E x))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.map_proj_nhds FiberBundle.map_proj_nhdsₓ'. -/
 theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
   (trivializationAt F E x.proj).map_proj_nhds <|
     (trivializationAt F E x.proj).mem_source.2 <| mem_baseSet_trivializationAt F E x.proj
@@ -231,17 +241,35 @@ theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
 
 variable (E)
 
+/- warning: fiber_bundle.continuous_proj -> FiberBundle.continuous_proj is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+but is expected to have type
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], Continuous.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_proj FiberBundle.continuous_projₓ'. -/
 /-- The projection from a fiber bundle to its base is continuous. -/
 @[continuity]
 theorem continuous_proj : Continuous (π E) :=
   continuous_iff_continuousAt.2 fun x => (map_proj_nhds F x).le
 #align fiber_bundle.continuous_proj FiberBundle.continuous_proj
 
+/- warning: fiber_bundle.is_open_map_proj -> FiberBundle.isOpenMap_proj is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], IsOpenMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+but is expected to have type
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)], IsOpenMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_projₓ'. -/
 /-- The projection from a fiber bundle to its base is an open map. -/
 theorem isOpenMap_proj : IsOpenMap (π E) :=
   IsOpenMap.of_nhds_le fun x => (map_proj_nhds F x).ge
 #align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_proj
 
+/- warning: fiber_bundle.surjective_proj -> FiberBundle.surjective_proj is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u2} F], Function.Surjective.{max (succ u1) (succ u3), succ u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E)
+but is expected to have type
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u3} F], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Bundle.TotalSpace.{u2, u1} B E) B (Bundle.TotalSpace.proj.{u2, u1} B E)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.surjective_proj FiberBundle.surjective_projₓ'. -/
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a surjective
 map. -/
 theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
@@ -250,12 +278,24 @@ theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
   ⟨p, hpb⟩
 #align fiber_bundle.surjective_proj FiberBundle.surjective_proj
 
+/- warning: fiber_bundle.quotient_map_proj -> FiberBundle.quotientMap_proj is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u2} F], QuotientMap.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+but is expected to have type
+  forall {B : Type.{u2}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u2} (Bundle.TotalSpace.{u2, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : FiberBundle.{u2, u3, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] [_inst_6 : Nonempty.{succ u3} F], QuotientMap.{max u2 u1, u2} (Bundle.TotalSpace.{u2, u1} B E) B _inst_3 _inst_1 (Bundle.TotalSpace.proj.{u2, u1} B E)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_projₓ'. -/
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a quotient
 map. -/
 theorem quotientMap_proj [Nonempty F] : QuotientMap (π E) :=
   (isOpenMap_proj F E).to_quotientMap (continuous_proj F E) (surjective_proj F E)
 #align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_proj
 
+/- warning: fiber_bundle.continuous_total_space_mk -> FiberBundle.continuous_totalSpaceMk is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : B), Continuous.{u3, max u1 u3} (E x) (Bundle.TotalSpace.{u1, u3} B E) (_inst_4 x) _inst_3 (Bundle.totalSpaceMk.{u1, u3} B E x)
+but is expected to have type
+  forall {B : Type.{u1}} (F : Type.{u3}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u3} F] (E : B -> Type.{u2}) [_inst_3 : TopologicalSpace.{max u2 u1} (Bundle.TotalSpace.{u1, u2} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u2} (E b)] [_inst_5 : FiberBundle.{u1, u3, u2} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (x : B), Continuous.{u2, max u1 u2} (E x) (Bundle.TotalSpace.{u1, u2} B E) (_inst_4 x) _inst_3 (Bundle.totalSpaceMk.{u1, u2} B E x)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMkₓ'. -/
 theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
   (totalSpaceMk_inducing F E x).Continuous
 #align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMk
@@ -264,6 +304,12 @@ end FiberBundle
 
 variable (F E)
 
+/- warning: fiber_bundle.exists_trivialization_Icc_subset -> FiberBundle.exists_trivialization_Icc_subset is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u3}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u3} (E b)] [_inst_5 : ConditionallyCompleteLinearOrder.{u1} B] [_inst_6 : OrderTopology.{u1} B _inst_1 (PartialOrder.toPreorder.{u1} B (SemilatticeInf.toPartialOrder.{u1} B (Lattice.toSemilatticeInf.{u1} B (ConditionallyCompleteLattice.toLattice.{u1} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} B _inst_5)))))] [_inst_7 : FiberBundle.{u1, u2, u3} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (a : B) (b : B), Exists.{max (succ u1) (succ u2) (succ (max u1 u3))} (Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) (fun (e : Trivialization.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E)) => HasSubset.Subset.{u1} (Set.{u1} B) (Set.hasSubset.{u1} B) (Set.Icc.{u1} B (PartialOrder.toPreorder.{u1} B (SemilatticeInf.toPartialOrder.{u1} B (Lattice.toSemilatticeInf.{u1} B (ConditionallyCompleteLattice.toLattice.{u1} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} B _inst_5))))) a b) (Trivialization.baseSet.{u1, u2, max u1 u3} B F (Bundle.TotalSpace.{u1, u3} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u1, u3} B E) e))
+but is expected to have type
+  forall {B : Type.{u3}} (F : Type.{u2}) [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (E : B -> Type.{u1}) [_inst_3 : TopologicalSpace.{max u1 u3} (Bundle.TotalSpace.{u3, u1} B E)] [_inst_4 : forall (b : B), TopologicalSpace.{u1} (E b)] [_inst_5 : ConditionallyCompleteLinearOrder.{u3} B] [_inst_6 : OrderTopology.{u3} B _inst_1 (PartialOrder.toPreorder.{u3} B (SemilatticeInf.toPartialOrder.{u3} B (Lattice.toSemilatticeInf.{u3} B (ConditionallyCompleteLattice.toLattice.{u3} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} B _inst_5)))))] [_inst_7 : FiberBundle.{u3, u2, u1} B F _inst_1 _inst_2 E _inst_3 (fun (b : B) => _inst_4 b)] (a : B) (b : B), Exists.{max (max (succ u3) (succ u2)) (succ u1)} (Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) (fun (e : Trivialization.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E)) => HasSubset.Subset.{u3} (Set.{u3} B) (Set.instHasSubsetSet.{u3} B) (Set.Icc.{u3} B (PartialOrder.toPreorder.{u3} B (SemilatticeInf.toPartialOrder.{u3} B (Lattice.toSemilatticeInf.{u3} B (ConditionallyCompleteLattice.toLattice.{u3} B (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} B _inst_5))))) a b) (Trivialization.baseSet.{u3, u2, max u3 u1} B F (Bundle.TotalSpace.{u3, u1} B E) _inst_1 _inst_2 _inst_3 (Bundle.TotalSpace.proj.{u3, u1} B E) e))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subsetₓ'. -/
 /-- If `E` is a fiber bundle over a conditionally complete linear order,
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
@@ -342,6 +388,7 @@ end FiberBundle
 /-! ### Core construction for constructing fiber bundles -/
 
 
+#print FiberBundleCore /-
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Core data defining a locally trivial bundle with fiber `F` over a topological
 space `B`. Note that "bundle" is used in its mathematical sense. This is the (computer science)
@@ -368,6 +415,7 @@ structure FiberBundleCore (ι : Type _) (B : Type _) [TopologicalSpace B] (F : T
       ∀ x ∈ base_set i ∩ base_set j ∩ base_set k,
         ∀ v, (coord_change j k x) (coord_change i j x v) = coord_change i k x v
 #align fiber_bundle_core FiberBundleCore
+-/
 
 namespace FiberBundleCore
 
@@ -375,34 +423,43 @@ variable [TopologicalSpace B] [TopologicalSpace F] (Z : FiberBundleCore ι B F)
 
 include Z
 
+#print FiberBundleCore.Index /-
 /-- The index set of a fiber bundle core, as a convenience function for dot notation -/
 @[nolint unused_arguments has_nonempty_instance]
 def Index :=
   ι
 #align fiber_bundle_core.index FiberBundleCore.Index
+-/
 
+#print FiberBundleCore.Base /-
 /-- The base space of a fiber bundle core, as a convenience function for dot notation -/
 @[nolint unused_arguments, reducible]
 def Base :=
   B
 #align fiber_bundle_core.base FiberBundleCore.Base
+-/
 
+#print FiberBundleCore.Fiber /-
 /-- The fiber of a fiber bundle core, as a convenience function for dot notation and
 typeclass inference -/
 @[nolint unused_arguments has_nonempty_instance]
 def Fiber (x : B) :=
   F
 #align fiber_bundle_core.fiber FiberBundleCore.Fiber
+-/
 
 section FiberInstances
 
 attribute [local reducible] fiber
 
+#print FiberBundleCore.topologicalSpaceFiber /-
 instance topologicalSpaceFiber (x : B) : TopologicalSpace (Z.Fiber x) := by infer_instance
 #align fiber_bundle_core.topological_space_fiber FiberBundleCore.topologicalSpaceFiber
+-/
 
 end FiberInstances
 
+#print FiberBundleCore.TotalSpace /-
 /-- The total space of the fiber bundle, as a convenience function for dot notation.
 It is by definition equal to `bundle.total_space Z.fiber`, a.k.a. `Σ x, Z.fiber x` but with a
 different name for typeclass inference. -/
@@ -410,13 +467,22 @@ different name for typeclass inference. -/
 def TotalSpace :=
   Bundle.TotalSpace Z.Fiber
 #align fiber_bundle_core.total_space FiberBundleCore.TotalSpace
+-/
 
+#print FiberBundleCore.proj /-
 /-- The projection from the total space of a fiber bundle core, on its base. -/
 @[reducible, simp, mfld_simps]
 def proj : Z.TotalSpace → B :=
   Bundle.TotalSpace.proj
 #align fiber_bundle_core.proj FiberBundleCore.proj
+-/
 
+/- warning: fiber_bundle_core.triv_change -> FiberBundleCore.trivChange is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F], (FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) -> ι -> ι -> (LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F], (FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) -> ι -> ι -> (LocalHomeomorph.{max u3 u2, max u3 u2} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (instTopologicalSpaceProd.{u2, u3} B F _inst_1 _inst_2) (instTopologicalSpaceProd.{u2, u3} B F _inst_1 _inst_2))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.triv_change FiberBundleCore.trivChangeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Local homeomorphism version of the trivialization change. -/
@@ -448,6 +514,12 @@ def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F)
       ContinuousOn.prod continuous_fst.continuous_on (Z.continuous_on_coord_change j i)
 #align fiber_bundle_core.triv_change FiberBundleCore.trivChange
 
+/- warning: fiber_bundle_core.mem_triv_change_source -> FiberBundleCore.mem_trivChange_source is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (j : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i j)))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Inter.inter.{u2} (Set.{u2} B) (Set.hasInter.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z j)))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (j : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.source.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i j)))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_1 F _inst_2 Z i) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_1 F _inst_2 Z j)))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_triv_change_source FiberBundleCore.mem_trivChange_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_trivChange_source (i j : ι) (p : B × F) :
     p ∈ (Z.trivChange i j).source ↔ p.1 ∈ Z.baseSet i ∩ Z.baseSet j :=
@@ -457,6 +529,7 @@ theorem mem_trivChange_source (i j : ι) (p : B × F) :
 #align fiber_bundle_core.mem_triv_change_source FiberBundleCore.mem_trivChange_source
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberBundleCore.localTrivAsLocalEquiv /-
 /-- Associate to a trivialization index `i : ι` the corresponding trivialization, i.e., a bijection
 between `proj ⁻¹ (base_set i)` and `base_set i × F`. As the fiber above `x` is `F` but read in the
 chart with index `index_at x`, the trivialization in the fiber above x is by definition the
@@ -489,14 +562,27 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F)
     · exact hx
     · simp only [hx, mem_inter_iff, and_self_iff, mem_base_set_at]
 #align fiber_bundle_core.local_triv_as_local_equiv FiberBundleCore.localTrivAsLocalEquiv
+-/
 
 variable (i : ι)
 
+/- warning: fiber_bundle_core.mem_local_triv_as_local_equiv_source -> FiberBundleCore.mem_localTrivAsLocalEquiv_source is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Set.hasMem.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) p (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i))
+but is expected to have type
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Set.instMembershipSet.{max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) p (LocalEquiv.source.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u1} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.baseSet.{u3, u2, u1} ι B _inst_1 F _inst_2 Z i))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_sourceₓ'. -/
 theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
 
+/- warning: fiber_bundle_core.mem_local_triv_as_local_equiv_target -> FiberBundleCore.mem_localTrivAsLocalEquiv_target is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.baseSet.{u1, u3, u2} ι B _inst_1 F _inst_2 Z i))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_targetₓ'. -/
 theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
     p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i :=
   by
@@ -504,11 +590,23 @@ theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
   simp only [and_true_iff, mem_univ]
 #align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_target
 
+/- warning: fiber_bundle_core.local_triv_as_local_equiv_apply -> FiberBundleCore.localTrivAsLocalEquiv_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (i : ι) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} B F) (LocalEquiv.toFun.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u1} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u3, u2, u1} ι B F _inst_1 _inst_2 Z i) p) (Prod.mk.{u2, u1} B F (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (FiberBundleCore.coordChange.{u3, u2, u1} ι B _inst_1 F _inst_2 Z (FiberBundleCore.indexAt.{u3, u2, u1} ι B _inst_1 F _inst_2 Z (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)) i (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Sigma.snd.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p)))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_applyₓ'. -/
 theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
     (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
 
+/- warning: fiber_bundle_core.local_triv_as_local_equiv_trans -> FiberBundleCore.localTrivAsLocalEquiv_trans is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (j : ι), HasEquivₓ.Equiv.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F)) (setoidHasEquiv.{succ (max u2 u3)} (LocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F)) (LocalEquiv.eqOnSourceSetoid.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F))) (LocalEquiv.trans.{max u2 u3, max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalEquiv.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z j)) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Prod.{u2, u3} B F) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.trivChange.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i j))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_transₓ'. -/
 /-- The composition of two local trivializations is the trivialization change Z.triv_change i j. -/
 theorem localTrivAsLocalEquiv_trans (i j : ι) :
     (Z.localTrivAsLocalEquiv i).symm.trans (Z.localTrivAsLocalEquiv j) ≈
@@ -526,15 +624,23 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
     simp only [Z.coord_change_comp, hx, mem_inter_iff, and_self_iff, mem_base_set_at]
 #align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_trans
 
+#print FiberBundleCore.toTopologicalSpace /-
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
 that all the local trivialization are continuous. -/
 instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace Z.Fiber) :=
   TopologicalSpace.generateFrom <|
     ⋃ (i : ι) (s : Set (B × F)) (s_open : IsOpen s), {(Z i).source ∩ Z i ⁻¹' s}
 #align fiber_bundle_core.to_topological_space FiberBundleCore.toTopologicalSpace
+-/
 
 variable (b : B) (a : F)
 
+/- warning: fiber_bundle_core.open_source' -> FiberBundleCore.open_source' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι), IsOpen.{max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (LocalEquiv.source.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι), IsOpen.{max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (LocalEquiv.source.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.localTrivAsLocalEquiv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.open_source' FiberBundleCore.open_source'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
   by
@@ -546,6 +652,7 @@ theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source :=
     mem_local_triv_as_local_equiv_source, and_true_iff, mem_univ, mem_preimage]
 #align fiber_bundle_core.open_source' FiberBundleCore.open_source'
 
+#print FiberBundleCore.localTriv /-
 /-- Extended version of the local trivialization of a fiber bundle constructed from core,
 registering additionally in its type that it is a local bundle trivialization. -/
 def localTriv (i : ι) : Trivialization F Z.proj
@@ -592,18 +699,33 @@ def localTriv (i : ι) : Trivialization F Z.proj
     rfl
   toLocalEquiv := Z.localTrivAsLocalEquiv i
 #align fiber_bundle_core.local_triv FiberBundleCore.localTriv
+-/
 
+#print FiberBundleCore.localTrivAt /-
 /-- Preferred local trivialization of a fiber bundle constructed from core, at a given point, as
 a bundle trivialization -/
 def localTrivAt (b : B) : Trivialization F (π Z.Fiber) :=
   Z.localTriv (Z.indexAt b)
 #align fiber_bundle_core.local_triv_at FiberBundleCore.localTrivAt
+-/
 
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 @[simp, mfld_simps]
 theorem localTrivAt_def (b : B) : Z.localTriv (Z.indexAt b) = Z.localTrivAt b :=
   rfl
 #align fiber_bundle_core.local_triv_at_def FiberBundleCore.localTrivAt_def
 
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 /-- If an element of `F` is invariant under all coordinate changes, then one can define a
 corresponding section of the fiber bundle, which is continuous. This applies in particular to the
 zero section of a vector bundle. Another example (not yet defined) would be the identity
@@ -625,40 +747,82 @@ theorem continuous_const_section (v : F)
   · exact A
 #align fiber_bundle_core.continuous_const_section FiberBundleCore.continuous_const_section
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv i :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsLocalEquiv_coe
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_source :
     (Z.localTrivAsLocalEquiv i).source = (Z.localTriv i).source :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsLocalEquiv_source
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_target :
     (Z.localTrivAsLocalEquiv i).target = (Z.localTriv i).target :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsLocalEquiv_target
 
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 @[simp, mfld_simps]
 theorem localTrivAsLocalEquiv_symm :
     (Z.localTrivAsLocalEquiv i).symm = (Z.localTriv i).toLocalEquiv.symm :=
   rfl
 #align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsLocalEquiv_symm
 
+/- warning: fiber_bundle_core.base_set_at -> FiberBundleCore.baseSet_at is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ u2} (Set.{u2} B) (FiberBundleCore.baseSet.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))
+but is expected to have type
+  forall {ι : Type.{u2}} {B : Type.{u3}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u2, u3, u1} ι B _inst_1 F _inst_2) (i : ι), Eq.{succ u3} (Set.{u3} B) (FiberBundleCore.baseSet.{u2, u3, u1} ι B _inst_1 F _inst_2 Z i) (Trivialization.baseSet.{u3, u1, max u3 u1} B F (FiberBundleCore.TotalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u2, u3, u1} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u2, u3, u1} ι B F _inst_1 _inst_2 Z i))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.base_set_at FiberBundleCore.baseSet_atₓ'. -/
 @[simp, mfld_simps]
 theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
   rfl
 #align fiber_bundle_core.base_set_at FiberBundleCore.baseSet_at
 
+/- warning: fiber_bundle_core.local_triv_apply -> FiberBundleCore.localTriv_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_applyₓ'. -/
 @[simp, mfld_simps]
 theorem localTriv_apply (p : Z.TotalSpace) :
     (Z.localTriv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_apply FiberBundleCore.localTriv_apply
 
+/- warning: fiber_bundle_core.local_triv_at_apply -> FiberBundleCore.localTrivAt_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_applyₓ'. -/
 @[simp, mfld_simps]
 theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p.2⟩ :=
   by
@@ -666,23 +830,47 @@ theorem localTrivAt_apply (p : Z.TotalSpace) : (Z.localTrivAt p.1) p = ⟨p.1, p
   exact Z.mem_base_set_at p.1
 #align fiber_bundle_core.local_triv_at_apply FiberBundleCore.localTrivAt_apply
 
+/- warning: fiber_bundle_core.local_triv_at_apply_mk -> FiberBundleCore.localTrivAt_apply_mk is a dubious translation:
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 @[simp, mfld_simps]
 theorem localTrivAt_apply_mk (b : B) (a : F) : (Z.localTrivAt b) ⟨b, a⟩ = ⟨b, a⟩ :=
   Z.localTrivAt_apply _
 #align fiber_bundle_core.local_triv_at_apply_mk FiberBundleCore.localTrivAt_apply_mk
 
+/- warning: fiber_bundle_core.mem_local_triv_source -> FiberBundleCore.mem_localTriv_source is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTriv_source (p : Z.TotalSpace) :
     p ∈ (Z.localTriv i).source ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_source FiberBundleCore.mem_localTriv_source
 
+/- warning: fiber_bundle_core.mem_local_triv_at_source -> FiberBundleCore.mem_localTrivAt_source is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (p : FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (b : B), Iff (Membership.Mem.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) (Set.hasMem.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) p (LocalEquiv.source.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Sigma.fst.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b)))
+but is expected to have type
+  forall {ι : Type.{u3}} {B : Type.{u2}} {F : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (Z : FiberBundleCore.{u3, u2, u1} ι B _inst_1 F _inst_2) (p : FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (b : B), Iff (Membership.mem.{max u2 u1, max u2 u1} (FiberBundleCore.TotalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Set.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z))) (Set.instMembershipSet.{max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z))) p (LocalEquiv.source.{max u2 u1, max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u1} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u1, max u2 u1} (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u1} B F) (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u2, u1} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_1 _inst_2 Z b))))) (Membership.mem.{u2, u2} B (Set.{u2} B) (Set.instMembershipSet.{u2} B) (Sigma.fst.{u2, u1} B (fun (x : B) => FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z x) p) (Trivialization.baseSet.{u2, u1, max u2 u1} B F (Bundle.TotalSpace.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u3, u2, u1} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u1} B (FiberBundleCore.Fiber.{u3, u2, u1} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u3, u2, u1} ι B F _inst_1 _inst_2 Z b)))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_sourceₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
     p ∈ (Z.localTrivAt b).source ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_source
 
+/- warning: fiber_bundle_core.mem_source_at -> FiberBundleCore.mem_source_at is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (b : B) (a : F), Membership.Mem.{max u2 u3, max u2 u3} (Sigma.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x)) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) (Set.hasMem.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z))) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) b a) (LocalEquiv.source.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (b : B) (a : F), Membership.mem.{max u3 u2, max u3 u2} (Sigma.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x)) (Set.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z))) (Set.instMembershipSet.{max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z))) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x) b a) (LocalEquiv.source.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b))))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_atₓ'. -/
 @[simp, mfld_simps]
 theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source :=
   by
@@ -690,24 +878,48 @@ theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source
   exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
 
+/- warning: fiber_bundle_core.mem_local_triv_target -> FiberBundleCore.mem_localTriv_target is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u2, u3} B F), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i)))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u3, u2} B F), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Trivialization.baseSet.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i)))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_target FiberBundleCore.mem_localTriv_targetₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTriv_target (p : B × F) :
     p ∈ (Z.localTriv i).target ↔ p.1 ∈ (Z.localTriv i).baseSet :=
   Trivialization.mem_target _
 #align fiber_bundle_core.mem_local_triv_target FiberBundleCore.mem_localTriv_target
 
+/- warning: fiber_bundle_core.mem_local_triv_at_target -> FiberBundleCore.mem_localTrivAt_target is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (p : Prod.{u2, u3} B F) (b : B), Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (Set.{max u2 u3} (Prod.{u2, u3} B F)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} B F)) p (LocalEquiv.target.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (LocalHomeomorph.toLocalEquiv.{max u2 u3, max u2 u3} (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))))) (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) (Prod.fst.{u2, u3} B F p) (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b)))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (p : Prod.{u3, u2} B F) (b : B), Iff (Membership.mem.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} B F)) p (LocalEquiv.target.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (LocalHomeomorph.toLocalEquiv.{max u3 u2, max u3 u2} (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b))))) (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) (Prod.fst.{u3, u2} B F p) (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b)))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_target FiberBundleCore.mem_localTrivAt_targetₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTrivAt_target (p : B × F) (b : B) :
     p ∈ (Z.localTrivAt b).target ↔ p.1 ∈ (Z.localTrivAt b).baseSet :=
   Trivialization.mem_target _
 #align fiber_bundle_core.mem_local_triv_at_target FiberBundleCore.mem_localTrivAt_target
 
+/- warning: fiber_bundle_core.local_triv_symm_apply -> FiberBundleCore.localTriv_symm_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u2, u3} B F), Eq.{max (succ u2) (succ u3)} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (fun (_x : LocalHomeomorph.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) => (Prod.{u2, u3} B F) -> (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (LocalHomeomorph.hasCoeToFun.{max u2 u3, max u2 u3} (Prod.{u2, u3} B F) (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (LocalHomeomorph.symm.{max u2 u3, max u2 u3} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.{u2, u3} B F) (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Prod.topologicalSpace.{u2, u3} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u2, u3, max u2 u3} B F (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u2, u3} ι B F _inst_1 _inst_2 Z i))) p) (Sigma.mk.{u2, u3} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z x) (Prod.fst.{u2, u3} B F p) (FiberBundleCore.coordChange.{u1, u2, u3} ι B _inst_1 F _inst_2 Z i (FiberBundleCore.indexAt.{u1, u2, u3} ι B _inst_1 F _inst_2 Z (Prod.fst.{u2, u3} B F p)) (Prod.fst.{u2, u3} B F p) (Prod.snd.{u2, u3} B F p)))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (i : ι) (p : Prod.{u3, u2} B F), Eq.{max (succ u3) (succ u2)} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (LocalHomeomorph.toFun'.{max u3 u2, max u3 u2} (Prod.{u3, u2} B F) (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (LocalHomeomorph.symm.{max u3 u2, max u3 u2} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Prod.{u3, u2} B F) (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Trivialization.toLocalHomeomorph.{u3, u2, max u3 u2} B F (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (FiberBundleCore.localTriv.{u1, u3, u2} ι B F _inst_1 _inst_2 Z i))) p) (Sigma.mk.{u3, u2} B (fun (x : B) => FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z x) (Prod.fst.{u3, u2} B F p) (FiberBundleCore.coordChange.{u1, u3, u2} ι B _inst_1 F _inst_2 Z i (FiberBundleCore.indexAt.{u1, u3, u2} ι B _inst_1 F _inst_2 Z (Prod.fst.{u3, u2} B F p)) (Prod.fst.{u3, u2} B F p) (Prod.snd.{u3, u2} B F p)))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_applyₓ'. -/
 @[simp, mfld_simps]
 theorem localTriv_symm_apply (p : B × F) :
     (Z.localTriv i).toLocalHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_apply
 
+/- warning: fiber_bundle_core.mem_local_triv_at_base_set -> FiberBundleCore.mem_localTrivAt_baseSet is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2) (b : B), Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) b (Trivialization.baseSet.{u2, u3, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u2, u3} B (FiberBundleCore.Fiber.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u2, u3} ι B F _inst_1 _inst_2 Z b))
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2) (b : B), Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b (Trivialization.baseSet.{u3, u2, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) _inst_1 _inst_2 (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) (Bundle.TotalSpace.proj.{u3, u2} B (FiberBundleCore.Fiber.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)) (FiberBundleCore.localTrivAt.{u1, u3, u2} ι B F _inst_1 _inst_2 Z b))
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSetₓ'. -/
 @[simp, mfld_simps]
 theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet :=
   by
@@ -715,6 +927,7 @@ theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet :=
   exact Z.mem_base_set_at b
 #align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSet
 
+#print FiberBundleCore.continuous_totalSpaceMk /-
 /-- The inclusion of a fiber into the total space is a continuous map. -/
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
@@ -745,8 +958,10 @@ theorem continuous_totalSpaceMk (b : B) :
         preimage_empty, empty_inter]
       exact isOpen_empty
 #align fiber_bundle_core.continuous_total_space_mk FiberBundleCore.continuous_totalSpaceMk
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FiberBundleCore.fiberBundle /-
 /-- A fiber bundle constructed from core is indeed a fiber bundle. -/
 instance fiberBundle : FiberBundle F Z.Fiber
     where
@@ -773,12 +988,25 @@ instance fiberBundle : FiberBundle F Z.Fiber
   mem_baseSet_trivializationAt := Z.mem_baseSet_at
   trivialization_mem_atlas b := ⟨Z.indexAt b, rfl⟩
 #align fiber_bundle_core.fiber_bundle FiberBundleCore.fiberBundle
+-/
 
+/- warning: fiber_bundle_core.continuous_proj -> FiberBundleCore.continuous_proj is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2), Continuous.{max u2 u3, u2} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2), Continuous.{max u3 u2, u3} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.continuous_proj FiberBundleCore.continuous_projₓ'. -/
 /-- The projection on the base of a fiber bundle created from core is continuous -/
 theorem continuous_proj : Continuous Z.proj :=
   continuous_proj F Z.Fiber
 #align fiber_bundle_core.continuous_proj FiberBundleCore.continuous_proj
 
+/- warning: fiber_bundle_core.is_open_map_proj -> FiberBundleCore.isOpenMap_proj is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {B : Type.{u2}} {F : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u3} F] (Z : FiberBundleCore.{u1, u2, u3} ι B _inst_1 F _inst_2), IsOpenMap.{max u2 u3, u2} (FiberBundleCore.TotalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u2, u3} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u2, u3} ι B F _inst_1 _inst_2 Z)
+but is expected to have type
+  forall {ι : Type.{u1}} {B : Type.{u3}} {F : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u2} F] (Z : FiberBundleCore.{u1, u3, u2} ι B _inst_1 F _inst_2), IsOpenMap.{max u3 u2, u3} (FiberBundleCore.TotalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) B (FiberBundleCore.toTopologicalSpace.{u1, u3, u2} ι B F _inst_1 _inst_2 Z) _inst_1 (FiberBundleCore.proj.{u1, u3, u2} ι B F _inst_1 _inst_2 Z)
+Case conversion may be inaccurate. Consider using '#align fiber_bundle_core.is_open_map_proj FiberBundleCore.isOpenMap_projₓ'. -/
 /-- The projection on the base of a fiber bundle created from core is an open map -/
 theorem isOpenMap_proj : IsOpenMap Z.proj :=
   isOpenMap_proj F Z.Fiber
@@ -791,6 +1019,7 @@ end FiberBundleCore
 
 variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
 
+#print FiberPrebundle /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
@@ -806,17 +1035,26 @@ structure FiberPrebundle where
     ∀ (e) (_ : e ∈ pretrivialization_atlas) (e') (_ : e' ∈ pretrivialization_atlas),
       ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
 #align fiber_prebundle FiberPrebundle
+-/
 
 namespace FiberPrebundle
 
 variable {F E} (a : FiberPrebundle F E) {e : Pretrivialization F (π E)}
 
+#print FiberPrebundle.totalSpaceTopology /-
 /-- Topology on the total space that will make the prebundle into a bundle. -/
 def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E) :=
   ⨆ (e : Pretrivialization F (π E)) (he : e ∈ a.pretrivializationAtlas),
     coinduced e.setSymm Subtype.topologicalSpace
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
+-/
 
+/- warning: fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas -> FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) {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.{max u1 u2 u1 u3, max u1 u2 u1 u3} (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)) (Set.{max u1 u2 u1 u3} (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))) (Set.hasMem.{max u1 u2 u1 u3} (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))) e (FiberPrebundle.pretrivializationAtlas.{u1, u2, u3} B F E _inst_1 _inst_2 a)) -> (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) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (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))) (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)))
+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] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_1 _inst_2) {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.{max (max u3 u2) u1, max (max u3 u2) u1} (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)) (Set.{max (max (max u3 u1) u2) u3} (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))) (Set.instMembershipSet.{max (max u3 u2) u1} (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))) e (FiberPrebundle.pretrivializationAtlas.{u3, u2, u1} B F E _inst_1 _inst_2 a)) -> (ContinuousOn.{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) (FiberPrebundle.totalSpaceTopology.{u3, u2, u1} B F E _inst_1 _inst_2 a) (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))) (LocalEquiv.target.{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)))
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlasₓ'. -/
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target :=
   by
@@ -826,6 +1064,12 @@ theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializ
   exact le_supᵢ₂ e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
 
+/- warning: fiber_prebundle.is_open_source -> FiberPrebundle.isOpen_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (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)), IsOpen.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (LocalEquiv.source.{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))
+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] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_1 _inst_2) (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)), IsOpen.{max u3 u1} (Bundle.TotalSpace.{u3, u1} B E) (FiberPrebundle.totalSpaceTopology.{u3, u2, u1} B F E _inst_1 _inst_2 a) (LocalEquiv.source.{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))
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.is_open_source FiberPrebundle.isOpen_sourceₓ'. -/
 theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTopology] e.source :=
   by
   letI := a.total_space_topology
@@ -837,6 +1081,12 @@ theorem isOpen_source (e : Pretrivialization F (π E)) : is_open[a.totalSpaceTop
     Pretrivialization.preimage_symm_proj_inter]
 #align fiber_prebundle.is_open_source FiberPrebundle.isOpen_source
 
+/- warning: fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter -> FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (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)) (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.{max u1 u2 u1 u3, max u1 u2 u1 u3} (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)) (Set.{max u1 u2 u1 u3} (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))) (Set.hasMem.{max u1 u2 u1 u3} (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))) e' (FiberPrebundle.pretrivializationAtlas.{u1, u2, u3} B F E _inst_1 _inst_2 a)) -> (IsOpen.{max u1 u2} (Prod.{u1, u2} B F) (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) (Inter.inter.{max u1 u2} (Set.{max u1 u2} (Prod.{u1, u2} B F)) (Set.hasInter.{max u1 u2} (Prod.{u1, u2} B F)) (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')) (Set.preimage.{max u1 u2, max u1 u3} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) (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'))) (LocalEquiv.source.{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)))))
+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] (a : FiberPrebundle.{u3, u2, u1} B F E _inst_1 _inst_2) (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)) (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.{max (max u3 u2) u1, max (max u3 u2) u1} (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)) (Set.{max (max (max u3 u1) u2) u3} (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))) (Set.instMembershipSet.{max (max u3 u2) u1} (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))) e' (FiberPrebundle.pretrivializationAtlas.{u3, u2, u1} B F E _inst_1 _inst_2 a)) -> (IsOpen.{max u3 u2} (Prod.{u3, u2} B F) (instTopologicalSpaceProd.{u3, u2} B F _inst_1 _inst_2) (Inter.inter.{max u3 u2} (Set.{max u3 u2} (Prod.{u3, u2} B F)) (Set.instInterSet.{max u3 u2} (Prod.{u3, u2} B F)) (LocalEquiv.target.{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')) (Set.preimage.{max u3 u2, max u3 u1} (Prod.{u3, u2} B F) (Bundle.TotalSpace.{u3, u1} B E) (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'))) (LocalEquiv.source.{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)))))
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_interₓ'. -/
 theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π E))
     (he' : e' ∈ a.pretrivializationAtlas) :
     IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) :=
@@ -849,6 +1099,7 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
   exact hu1.inter e'.open_target
 #align fiber_prebundle.is_open_target_of_mem_pretrivialization_atlas_inter FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter
 
+#print FiberPrebundle.trivializationOfMemPretrivializationAtlas /-
 /-- Promotion from a `pretrivialization` to a `trivialization`. -/
 def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @Trivialization B F _ _ _ a.totalSpaceTopology (π E) :=
@@ -876,14 +1127,27 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       exact hu1.inter (a.is_open_target_of_mem_pretrivialization_atlas_inter e e' he')
     continuous_invFun := a.continuous_symm_of_mem_pretrivializationAtlas he }
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
+-/
 
-theorem mem_trivialization_at_source (b : B) (x : E b) :
+/- warning: fiber_prebundle.mem_trivialization_at_source -> FiberPrebundle.mem_pretrivializationAt_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B) (x : E b), Membership.Mem.{max u1 u3, max u1 u3} (Bundle.TotalSpace.{u1, u3} B (fun (b : B) => E b)) (Set.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Set.hasMem.{max u1 u3} (Bundle.TotalSpace.{u1, u3} B E)) (Bundle.totalSpaceMk.{u1, u3} B (fun (b : B) => E b) b x) (LocalEquiv.source.{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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b)))
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B) (x : E b), Membership.mem.{max u3 u2, max u2 u3} (Bundle.TotalSpace.{u2, u3} B E) (Set.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B E)) (Set.instMembershipSet.{max u2 u3} (Bundle.TotalSpace.{u2, u3} B E)) (Bundle.totalSpaceMk.{u2, u3} B E b x) (LocalEquiv.source.{max u2 u3, max u2 u1} (Bundle.TotalSpace.{u2, u3} B E) (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u3} B E) (FiberPrebundle.pretrivializationAt.{u2, u1, u3} B F E _inst_1 _inst_2 a b)))
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_pretrivializationAt_sourceₓ'. -/
+theorem mem_pretrivializationAt_source (b : B) (x : E b) :
     totalSpaceMk b x ∈ (a.pretrivializationAt b).source :=
   by
   simp only [(a.pretrivialization_at b).source_eq, mem_preimage, total_space.proj]
   exact a.mem_base_pretrivialization_at b
-#align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_trivialization_at_source
-
+#align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_pretrivializationAt_source
+
+/- warning: fiber_prebundle.total_space_mk_preimage_source -> FiberPrebundle.totalSpaceMk_preimage_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B), Eq.{succ u3} (Set.{u3} (E b)) (Set.preimage.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (Bundle.totalSpaceMk.{u1, u3} B E b) (LocalEquiv.source.{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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b)))) (Set.univ.{u3} (E b))
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B), Eq.{succ u3} (Set.{u3} (E b)) (Set.preimage.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (Bundle.totalSpaceMk.{u2, u3} B E b) (LocalEquiv.source.{max u2 u3, max u2 u1} (Bundle.TotalSpace.{u2, u3} B E) (Prod.{u2, u1} B F) (Pretrivialization.toLocalEquiv.{u2, u1, max u2 u3} B F (Bundle.TotalSpace.{u2, u3} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u2, u3} B E) (FiberPrebundle.pretrivializationAt.{u2, u1, u3} B F E _inst_1 _inst_2 a b)))) (Set.univ.{u3} (E b))
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_sourceₓ'. -/
 @[simp]
 theorem totalSpaceMk_preimage_source (b : B) :
     totalSpaceMk b ⁻¹' (a.pretrivializationAt b).source = univ :=
@@ -895,11 +1159,19 @@ theorem totalSpaceMk_preimage_source (b : B) :
   exact a.mem_base_pretrivialization_at b
 #align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_source
 
+#print FiberPrebundle.fiberTopology /-
 /-- Topology on the fibers `E b` induced by the map `E b → E.total_space`. -/
 def fiberTopology (b : B) : TopologicalSpace (E b) :=
   TopologicalSpace.induced (totalSpaceMk b) a.totalSpaceTopology
 #align fiber_prebundle.fiber_topology FiberPrebundle.fiberTopology
+-/
 
+/- warning: fiber_prebundle.inducing_total_space_mk -> FiberPrebundle.inducing_totalSpaceMk 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B), Inducing.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.fiberTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u1, u3} B E b)
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B), Inducing.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (FiberPrebundle.fiberTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u2, u3} B E b)
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMkₓ'. -/
 @[continuity]
 theorem inducing_totalSpaceMk (b : B) :
     @Inducing _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) :=
@@ -909,6 +1181,12 @@ theorem inducing_totalSpaceMk (b : B) :
   exact ⟨rfl⟩
 #align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMk
 
+/- warning: fiber_prebundle.continuous_total_space_mk -> FiberPrebundle.continuous_totalSpaceMk 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) (b : B), Continuous.{u3, max u1 u3} (E b) (Bundle.TotalSpace.{u1, u3} B E) (FiberPrebundle.fiberTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u1, u3} B E b)
+but is expected to have type
+  forall {B : Type.{u2}} {F : Type.{u1}} {E : B -> Type.{u3}} [_inst_1 : TopologicalSpace.{u2} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u2, u1, u3} B F E _inst_1 _inst_2) (b : B), Continuous.{u3, max u2 u3} (E b) (Bundle.TotalSpace.{u2, u3} B E) (FiberPrebundle.fiberTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a b) (FiberPrebundle.totalSpaceTopology.{u2, u1, u3} B F E _inst_1 _inst_2 a) (Bundle.totalSpaceMk.{u2, u3} B E b)
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMkₓ'. -/
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
     @Continuous _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) :=
@@ -917,6 +1195,7 @@ theorem continuous_totalSpaceMk (b : B) :
   exact (a.inducing_total_space_mk b).Continuous
 #align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMk
 
+#print FiberPrebundle.toFiberBundle /-
 /-- Make a `fiber_bundle` from a `fiber_prebundle`.  Concretely this means
 that, given a `fiber_prebundle` structure for a sigma-type `E` -- which consists of a
 number of "pretrivializations" identifying parts of `E` with product spaces `U × F` -- one
@@ -935,7 +1214,14 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology
   mem_baseSet_trivializationAt := a.mem_base_pretrivializationAt
   trivialization_mem_atlas x := ⟨_, a.pretrivialization_mem_atlas x, rfl⟩
 #align fiber_prebundle.to_fiber_bundle FiberPrebundle.toFiberBundle
+-/
 
+/- warning: fiber_prebundle.continuous_proj -> FiberPrebundle.continuous_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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2), Continuous.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) _inst_1 (Bundle.TotalSpace.proj.{u1, u3} B E)
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_1 _inst_2), Continuous.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_1 _inst_2 a) _inst_1 (Bundle.TotalSpace.proj.{u3, u2} B E)
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_proj FiberPrebundle.continuous_projₓ'. -/
 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   by
   letI := a.total_space_topology
@@ -944,6 +1230,12 @@ theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) :=
   exact continuous_proj F E
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj
 
+/- warning: fiber_prebundle.continuous_on_of_comp_right -> FiberPrebundle.continuousOn_of_comp_right 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] (a : FiberPrebundle.{u1, u2, u3} B F E _inst_1 _inst_2) {X : Type.{u4}} [_inst_3 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u1, u3} B E) -> X} {s : Set.{u1} B}, (IsOpen.{u1} B _inst_1 s) -> (forall (b : B), (Membership.Mem.{u1, u1} B (Set.{u1} B) (Set.hasMem.{u1} B) b s) -> (ContinuousOn.{max u1 u2, u4} (Prod.{u1, u2} B F) X (Prod.topologicalSpace.{u1, u2} B F _inst_1 _inst_2) _inst_3 (Function.comp.{succ (max u1 u2), max (succ u1) (succ u3), succ u4} (Prod.{u1, u2} B F) (Bundle.TotalSpace.{u1, u3} B E) X f (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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b))))) (Set.prod.{u1, u2} B F (Inter.inter.{u1} (Set.{u1} B) (Set.hasInter.{u1} B) s (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) (FiberPrebundle.pretrivializationAt.{u1, u2, u3} B F E _inst_1 _inst_2 a b))) (Set.univ.{u2} F)))) -> (ContinuousOn.{max u1 u3, u4} (Bundle.TotalSpace.{u1, u3} B E) X (FiberPrebundle.totalSpaceTopology.{u1, u2, u3} B F E _inst_1 _inst_2 a) _inst_3 f (Set.preimage.{max u1 u3, u1} (Bundle.TotalSpace.{u1, u3} B E) B (Bundle.TotalSpace.proj.{u1, u3} B E) s))
+but is expected to have type
+  forall {B : Type.{u3}} {F : Type.{u1}} {E : B -> Type.{u2}} [_inst_1 : TopologicalSpace.{u3} B] [_inst_2 : TopologicalSpace.{u1} F] (a : FiberPrebundle.{u3, u1, u2} B F E _inst_1 _inst_2) {X : Type.{u4}} [_inst_3 : TopologicalSpace.{u4} X] {f : (Bundle.TotalSpace.{u3, u2} B E) -> X} {s : Set.{u3} B}, (IsOpen.{u3} B _inst_1 s) -> (forall (b : B), (Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) b s) -> (ContinuousOn.{max u3 u1, u4} (Prod.{u3, u1} B F) X (instTopologicalSpaceProd.{u3, u1} B F _inst_1 _inst_2) _inst_3 (Function.comp.{succ (max u3 u1), max (succ u3) (succ u2), succ u4} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) X f (LocalEquiv.toFun.{max u3 u1, max u3 u2} (Prod.{u3, u1} B F) (Bundle.TotalSpace.{u3, u2} B E) (LocalEquiv.symm.{max u3 u2, max u3 u1} (Bundle.TotalSpace.{u3, u2} B E) (Prod.{u3, u1} B F) (Pretrivialization.toLocalEquiv.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_1 _inst_2 a b))))) (Set.prod.{u3, u1} B F (Inter.inter.{u3} (Set.{u3} B) (Set.instInterSet.{u3} B) s (Pretrivialization.baseSet.{u3, u1, max u3 u2} B F (Bundle.TotalSpace.{u3, u2} B E) _inst_1 _inst_2 (Bundle.TotalSpace.proj.{u3, u2} B E) (FiberPrebundle.pretrivializationAt.{u3, u1, u2} B F E _inst_1 _inst_2 a b))) (Set.univ.{u1} F)))) -> (ContinuousOn.{max u3 u2, u4} (Bundle.TotalSpace.{u3, u2} B E) X (FiberPrebundle.totalSpaceTopology.{u3, u1, u2} B F E _inst_1 _inst_2 a) _inst_3 f (Set.preimage.{max u3 u2, u3} (Bundle.TotalSpace.{u3, u2} B E) B (Bundle.TotalSpace.proj.{u3, u2} B E) s))
+Case conversion may be inaccurate. Consider using '#align fiber_prebundle.continuous_on_of_comp_right FiberPrebundle.continuousOn_of_comp_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- For a fiber bundle `E` over `B` constructed using the `fiber_prebundle` mechanism,
 continuity of a function `total_space E → X` on an open set `s` can be checked by precomposing at

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit bcfa726826abd57587355b4b5b7e78ad6527b7e4
+! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -85,24 +85,24 @@ typeclass containing data)?
 In their initial mathlib implementations, both fiber and vector bundles were defined
 propositionally. For vector bundles, this turns out to be mathematically wrong: in infinite
 dimension, the transition function between two trivializations is not automatically continuous as a
-map from the base `B` to the endomorphisms `F →L[R] F` of the fibre (considered with the
+map from the base `B` to the endomorphisms `F →L[R] F` of the fiber (considered with the
 operator-norm topology), and so the definition needs to be modified by restricting consideration to
 a family of trivializations (constituting the data) which are all mutually-compatible in this sense.
 The PRs #13052 and #13175 implemented this change.
 
 There is still the choice about whether to hold this data at the level of fiber bundles or of vector
 bundles. As of PR #17505, the data is all held in `fiber_bundle`, with `vector_bundle` a
-(propositional) mixin stating fibrewise-linearity.
+(propositional) mixin stating fiberwise-linearity.
 
 This allows bundles to carry instances of typeclasses in which the scalar field, `R`, does not
-appear as a parameter. Notably, we would like a vector bundle over `R` with fibre `F` over base `B`
+appear as a parameter. Notably, we would like a vector bundle over `R` with fiber `F` over base `B`
 to be a `charted_space (B × F)`, with the trivializations providing the charts. This would be a
 dangerous instance for typeclass inference, because `R` does not appear as a parameter in
 `charted_space (B × F)`. But if the data of the trivializations is held in `fiber_bundle`, then a
-fibre bundle with fibre `F` over base `B` can be a `charted_space (B × F)`, and this is safe for
+fiber bundle with fiber `F` over base `B` can be a `charted_space (B × F)`, and this is safe for
 typeclass inference.
 
-We expect that this choice of definition will also streamline constructions of fibre bundles with
+We expect that this choice of definition will also streamline constructions of fiber bundles with
 similar underlying structure (e.g., the same bundle being both a real and complex vector bundle).
 
 ### Core construction
@@ -210,7 +210,7 @@ variable {F E}
 /-- Given a type `E` equipped with a fiber bundle structure, this is a `Prop` typeclass
 for trivializations of `E`, expressing that a trivialization is in the designated atlas for the
 bundle.  This is needed because lemmas about the linearity of trivializations or the continuity (as
-functions to `F →L[R] F`, where `F` is the model fibre) of the transition functions are only
+functions to `F →L[R] F`, where `F` is the model fiber) of the transition functions are only
 expected to hold for trivializations in the designated atlas. -/
 @[mk_iff]
 class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π E)) : Prop where

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -791,7 +791,7 @@ end FiberBundleCore
 
 variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (e e' «expr ∈ » pretrivialization_atlas) -/
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the local equivalences

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

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.

@@ -393,7 +393,7 @@ Trivialization changes from `i` to `j` are given by continuous maps `coordChange
 `baseSet i ∩ baseSet j` to the set of homeomorphisms of `F`, but we express them as maps
 `B → F → F` and require continuity on `(baseSet i ∩ baseSet j) × F` to avoid the topology on the
 space of continuous maps on `F`. -/
--- Porting note: was @[nolint has_nonempty_instance]
+-- Porting note(#5171): was @[nolint has_nonempty_instance]
 structure FiberBundleCore (ι : Type*) (B : Type*) [TopologicalSpace B] (F : Type*)
     [TopologicalSpace F] where
   baseSet : ι → Set B
@@ -413,7 +413,7 @@ namespace FiberBundleCore
 variable [TopologicalSpace B] [TopologicalSpace F] (Z : FiberBundleCore ι B F)
 
 /-- The index set of a fiber bundle core, as a convenience function for dot notation -/
-@[nolint unusedArguments] -- Porting note: was has_nonempty_instance
+@[nolint unusedArguments] -- Porting note(#5171): was has_nonempty_instance
 def Index (_Z : FiberBundleCore ι B F) := ι
 #align fiber_bundle_core.index FiberBundleCore.Index
 
@@ -424,7 +424,7 @@ def Base (_Z : FiberBundleCore ι B F) := B
 
 /-- The fiber of a fiber bundle core, as a convenience function for dot notation and
 typeclass inference -/
-@[nolint unusedArguments] -- Porting note: was has_nonempty_instance
+@[nolint unusedArguments] -- Porting note(#5171): was has_nonempty_instance
 def Fiber (_ : FiberBundleCore ι B F) (_x : B) := F
 #align fiber_bundle_core.fiber FiberBundleCore.Fiber
 
@@ -762,7 +762,7 @@ variable (F) (E : B → Type*) [TopologicalSpace B] [TopologicalSpace F]
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the partial equivalences
 are also partial homeomorphisms and hence local trivializations. -/
--- Porting note (#11215): TODO: was @[nolint has_nonempty_instance]
+-- Porting note (#5171): was @[nolint has_nonempty_instance]
 structure FiberPrebundle where
   pretrivializationAtlas : Set (Pretrivialization F (π F E))
   pretrivializationAt : B → Pretrivialization F (π F E)

This splits up the file Mathlib/Topology/Order/Basic.lean (currently > 2000 lines) into several smaller files.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 -/
 import Mathlib.Topology.FiberBundle.Trivialization
+import Mathlib.Topology.Order.LeftRightNhds
 
 #align_import topology.fiber_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
 

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

@@ -711,7 +711,7 @@ theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
   exact Z.mem_baseSet_at b
 #align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSet
 
--- Porting note: was @[simp, mfld_simps], now `simp` can prove it
+-- Porting note (#10618): was @[simp, mfld_simps], now `simp` can prove it
 theorem mk_mem_localTrivAt_source : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
   simp only [mfld_simps]
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_localTrivAt_source

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

@@ -761,7 +761,7 @@ variable (F) (E : B → Type*) [TopologicalSpace B] [TopologicalSpace F]
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the partial equivalences
 are also partial homeomorphisms and hence local trivializations. -/
--- Porting note: todo: was @[nolint has_nonempty_instance]
+-- Porting note (#11215): TODO: was @[nolint has_nonempty_instance]
 structure FiberPrebundle where
   pretrivializationAtlas : Set (Pretrivialization F (π F E))
   pretrivializationAt : B → Pretrivialization F (π F E)

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".

@@ -282,7 +282,7 @@ theorem mem_trivializationAt_proj_source {x : TotalSpace F E} :
   (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
 
--- porting note: removed `@[simp, mfld_simps]` because `simp` could already prove this
+-- Porting note: removed `@[simp, mfld_simps]` because `simp` could already prove this
 theorem trivializationAt_proj_fst {x : TotalSpace F E} :
     ((trivializationAt F E x.proj) x).1 = x.proj :=
   Trivialization.coe_fst' _ <| mem_baseSet_trivializationAt F E x.proj
@@ -392,7 +392,7 @@ Trivialization changes from `i` to `j` are given by continuous maps `coordChange
 `baseSet i ∩ baseSet j` to the set of homeomorphisms of `F`, but we express them as maps
 `B → F → F` and require continuity on `(baseSet i ∩ baseSet j) × F` to avoid the topology on the
 space of continuous maps on `F`. -/
--- porting note: was @[nolint has_nonempty_instance]
+-- Porting note: was @[nolint has_nonempty_instance]
 structure FiberBundleCore (ι : Type*) (B : Type*) [TopologicalSpace B] (F : Type*)
     [TopologicalSpace F] where
   baseSet : ι → Set B
@@ -412,7 +412,7 @@ namespace FiberBundleCore
 variable [TopologicalSpace B] [TopologicalSpace F] (Z : FiberBundleCore ι B F)
 
 /-- The index set of a fiber bundle core, as a convenience function for dot notation -/
-@[nolint unusedArguments] -- porting note: was has_nonempty_instance
+@[nolint unusedArguments] -- Porting note: was has_nonempty_instance
 def Index (_Z : FiberBundleCore ι B F) := ι
 #align fiber_bundle_core.index FiberBundleCore.Index
 
@@ -423,7 +423,7 @@ def Base (_Z : FiberBundleCore ι B F) := B
 
 /-- The fiber of a fiber bundle core, as a convenience function for dot notation and
 typeclass inference -/
-@[nolint unusedArguments] -- porting note: was has_nonempty_instance
+@[nolint unusedArguments] -- Porting note: was has_nonempty_instance
 def Fiber (_ : FiberBundleCore ι B F) (_x : B) := F
 #align fiber_bundle_core.fiber FiberBundleCore.Fiber
 
@@ -711,7 +711,7 @@ theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
   exact Z.mem_baseSet_at b
 #align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSet
 
--- porting note: was @[simp, mfld_simps], now `simp` can prove it
+-- Porting note: was @[simp, mfld_simps], now `simp` can prove it
 theorem mk_mem_localTrivAt_source : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
   simp only [mfld_simps]
 #align fiber_bundle_core.mem_source_at FiberBundleCore.mem_localTrivAt_source
@@ -761,7 +761,7 @@ variable (F) (E : B → Type*) [TopologicalSpace B] [TopologicalSpace F]
 equivalences but there is not yet a topology on the total space. The total space is hence given a
 topology in such a way that there is a fiber bundle structure for which the partial equivalences
 are also partial homeomorphisms and hence local trivializations. -/
--- porting note: todo: was @[nolint has_nonempty_instance]
+-- Porting note: todo: was @[nolint has_nonempty_instance]
 structure FiberPrebundle where
   pretrivializationAtlas : Set (Pretrivialization F (π F E))
   pretrivializationAt : B → Pretrivialization F (π F E)

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -591,7 +591,7 @@ def localTriv (i : ι) : Trivialization F Z.proj where
       exact (continuousOn_open_iff (Z.trivChange i j).open_source).1
         (Z.trivChange i j).continuousOn _ s_open
     convert this using 1
-    dsimp [PartialEquiv.trans_source]
+    dsimp [f, PartialEquiv.trans_source]
     rw [← preimage_comp, inter_assoc]
   toPartialEquiv := Z.localTrivAsPartialEquiv i
 #align fiber_bundle_core.local_triv FiberBundleCore.localTriv

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -347,7 +347,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
       `proj` over `[a, d]`. Then we can glue `ead` and `ec` into a trivialization over `[a, c]`. -/
     obtain ⟨d, ⟨hdab, ead, had⟩, hd⟩ : ∃ d ∈ s, d ∈ Ioc c' c := hsc.exists_between hc'.2
     refine' ⟨ead.piecewiseLe ec d (had ⟨hdab.1, le_rfl⟩) (hc'e hd), subset_ite.2 _⟩
-    refine' ⟨fun x hx => had ⟨hx.1.1, hx.2⟩, fun x hx => hc'e ⟨hd.1.trans (not_le.1 hx.2), hx.1.2⟩⟩
+    exact ⟨fun x hx => had ⟨hx.1.1, hx.2⟩, fun x hx => hc'e ⟨hd.1.trans (not_le.1 hx.2), hx.1.2⟩⟩
   /- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
     done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
     `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/

• @[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
• add Lean.Name.decapitalize
• fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

@@ -216,7 +216,7 @@ for trivializations of `E`, expressing that a trivialization is in the designate
 bundle.  This is needed because lemmas about the linearity of trivializations or the continuity (as
 functions to `F →L[R] F`, where `F` is the model fiber) of the transition functions are only
 expected to hold for trivializations in the designated atlas. -/
-@[mk_iff memTrivializationAtlas_iff]
+@[mk_iff]
 class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π F E)) : Prop where
   out : e ∈ trivializationAtlas F E
 #align mem_trivialization_atlas MemTrivializationAtlas

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.

@@ -39,7 +39,7 @@ an implementation of this construction: starting from an object of type
 fiber bundle and projection.
 
 Similarly we implement the object `FiberPrebundle` which allows to define a topological
-fiber bundle from trivializations given as local equivalences with minimum additional properties.
+fiber bundle from trivializations given as partial equivalences with minimum additional properties.
 
 ## Main definitions
 
@@ -64,7 +64,7 @@ Let `Z : FiberBundleCore ι B F`. Then we define
                     open set in `B`.
 
 * `FiberPrebundle F E` : structure registering a cover of prebundle trivializations
-  and requiring that the relative transition maps are local homeomorphisms.
+  and requiring that the relative transition maps are partial homeomorphisms.
 * `FiberPrebundle.totalSpaceTopology a` : natural topology of the total space, making
   the prebundle into a bundle.
 
@@ -481,7 +481,7 @@ theorem mem_trivChange_source (i j : ι) (p : B × F) :
 between `proj ⁻¹ (baseSet i)` and `baseSet i × F`. As the fiber above `x` is `F` but read in the
 chart with index `index_at x`, the trivialization in the fiber above x is by definition the
 coordinate change from i to `index_at x`, so it depends on `x`.
-The local trivialization will ultimately be a local homeomorphism. For now, we only introduce the
+The local trivialization will ultimately be a partial homeomorphism. For now, we only introduce the
 partial equivalence version, denoted with a prime.
 In further developments, avoid this auxiliary version, and use `Z.local_triv` instead. -/
 def localTrivAsPartialEquiv (i : ι) : PartialEquiv Z.TotalSpace (B × F) where
@@ -759,8 +759,8 @@ variable (F) (E : B → Type*) [TopologicalSpace B] [TopologicalSpace F]
 
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
-topology in such a way that there is a fiber bundle structure for which the local equivalences
-are also local homeomorphism and hence local trivializations. -/
+topology in such a way that there is a fiber bundle structure for which the partial equivalences
+are also partial homeomorphisms and hence local trivializations. -/
 -- porting note: todo: was @[nolint has_nonempty_instance]
 structure FiberPrebundle where
   pretrivializationAtlas : Set (Pretrivialization F (π F E))

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -333,7 +333,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   have hsc : IsLUB s c := isLUB_csSup sne sbd
   have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
   obtain ⟨-, ec : Trivialization F (π F E), hec : Icc a c ⊆ ec.baseSet⟩ : c ∈ s := by
-    cases' hc.1.eq_or_lt with heq hlt
+    rcases hc.1.eq_or_lt with heq | hlt
     · rwa [← heq]
     refine ⟨hc, ?_⟩
     /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
@@ -351,7 +351,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   /- So, `c ∈ s`. Let `ec` be a trivialization of `proj` over `[a, c]`.  If `c = b`, then we are
     done. Otherwise we show that `proj` can be trivialized over a larger interval `[a, d]`,
     `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
-  cases' hc.2.eq_or_lt with heq hlt
+  rcases hc.2.eq_or_lt with heq | hlt
   · exact ⟨ec, heq ▸ hec⟩
   rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
   · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim

Updates proofs that had been doing rsuffices manually.

@@ -353,9 +353,8 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
   cases' hc.2.eq_or_lt with heq hlt
   · exact ⟨ec, heq ▸ hec⟩
-  suffices : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
-  · rcases this with ⟨d, hdcb, hd⟩ -- porting note: todo: use `rsuffices`
-    exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
+  rsuffices ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
+  · exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
   /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
     `d ∈ (c, b]`. -/
   obtain ⟨d, hdcb, hd⟩ : ∃ d ∈ Ioc c b, Ico c d ⊆ ec.baseSet :=

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>

@@ -483,10 +483,9 @@ between `proj ⁻¹ (baseSet i)` and `baseSet i × F`. As the fiber above `x` is
 chart with index `index_at x`, the trivialization in the fiber above x is by definition the
 coordinate change from i to `index_at x`, so it depends on `x`.
 The local trivialization will ultimately be a local homeomorphism. For now, we only introduce the
-local equiv version, denoted with a prime. In further developments, avoid this auxiliary version,
-and use `Z.local_triv` instead.
--/
-def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F) where
+partial equivalence version, denoted with a prime.
+In further developments, avoid this auxiliary version, and use `Z.local_triv` instead. -/
+def localTrivAsPartialEquiv (i : ι) : PartialEquiv Z.TotalSpace (B × F) where
   source := Z.proj ⁻¹' Z.baseSet i
   target := Z.baseSet i ×ˢ univ
   invFun p := ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩
@@ -506,58 +505,58 @@ def localTrivAsLocalEquiv (i : ι) : LocalEquiv Z.TotalSpace (B × F) where
     dsimp only
     rw [Z.coordChange_comp, Z.coordChange_self]
     exacts [hx, ⟨⟨hx, Z.mem_baseSet_at _⟩, hx⟩]
-#align fiber_bundle_core.local_triv_as_local_equiv FiberBundleCore.localTrivAsLocalEquiv
+#align fiber_bundle_core.local_triv_as_local_equiv FiberBundleCore.localTrivAsPartialEquiv
 
 variable (i : ι)
 
-theorem mem_localTrivAsLocalEquiv_source (p : Z.TotalSpace) :
-    p ∈ (Z.localTrivAsLocalEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
+theorem mem_localTrivAsPartialEquiv_source (p : Z.TotalSpace) :
+    p ∈ (Z.localTrivAsPartialEquiv i).source ↔ p.1 ∈ Z.baseSet i :=
   Iff.rfl
-#align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsLocalEquiv_source
+#align fiber_bundle_core.mem_local_triv_as_local_equiv_source FiberBundleCore.mem_localTrivAsPartialEquiv_source
 
-theorem mem_localTrivAsLocalEquiv_target (p : B × F) :
-    p ∈ (Z.localTrivAsLocalEquiv i).target ↔ p.1 ∈ Z.baseSet i := by
+theorem mem_localTrivAsPartialEquiv_target (p : B × F) :
+    p ∈ (Z.localTrivAsPartialEquiv i).target ↔ p.1 ∈ Z.baseSet i := by
   erw [mem_prod]
   simp only [and_true_iff, mem_univ]
-#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsLocalEquiv_target
+#align fiber_bundle_core.mem_local_triv_as_local_equiv_target FiberBundleCore.mem_localTrivAsPartialEquiv_target
 
-theorem localTrivAsLocalEquiv_apply (p : Z.TotalSpace) :
-    (Z.localTrivAsLocalEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
+theorem localTrivAsPartialEquiv_apply (p : Z.TotalSpace) :
+    (Z.localTrivAsPartialEquiv i) p = ⟨p.1, Z.coordChange (Z.indexAt p.1) i p.1 p.2⟩ :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsLocalEquiv_apply
+#align fiber_bundle_core.local_triv_as_local_equiv_apply FiberBundleCore.localTrivAsPartialEquiv_apply
 
 /-- The composition of two local trivializations is the trivialization change Z.triv_change i j. -/
-theorem localTrivAsLocalEquiv_trans (i j : ι) :
-    (Z.localTrivAsLocalEquiv i).symm.trans (Z.localTrivAsLocalEquiv j) ≈
-      (Z.trivChange i j).toLocalEquiv := by
+theorem localTrivAsPartialEquiv_trans (i j : ι) :
+    (Z.localTrivAsPartialEquiv i).symm.trans (Z.localTrivAsPartialEquiv j) ≈
+      (Z.trivChange i j).toPartialEquiv := by
   constructor
   · ext x
-    simp only [mem_localTrivAsLocalEquiv_target, mfld_simps]
+    simp only [mem_localTrivAsPartialEquiv_target, mfld_simps]
     rfl
   · rintro ⟨x, v⟩ hx
-    simp only [trivChange, localTrivAsLocalEquiv, LocalEquiv.symm, true_and_iff,
-      Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, LocalEquiv.trans_source, mem_inter_iff,
+    simp only [trivChange, localTrivAsPartialEquiv, PartialEquiv.symm, true_and_iff,
+      Prod.mk.inj_iff, prod_mk_mem_set_prod_eq, PartialEquiv.trans_source, mem_inter_iff,
       and_true_iff, mem_preimage, proj, mem_univ, eq_self_iff_true, (· ∘ ·),
-      LocalEquiv.coe_trans, TotalSpace.proj] at hx ⊢
+      PartialEquiv.coe_trans, TotalSpace.proj] at hx ⊢
     simp only [Z.coordChange_comp, hx, mem_inter_iff, and_self_iff, mem_baseSet_at]
-#align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsLocalEquiv_trans
+#align fiber_bundle_core.local_triv_as_local_equiv_trans FiberBundleCore.localTrivAsPartialEquiv_trans
 
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
 that all the local trivialization are continuous. -/
 instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace F Z.Fiber) :=
   TopologicalSpace.generateFrom <| ⋃ (i : ι) (s : Set (B × F)) (_ : IsOpen s),
-    {(Z.localTrivAsLocalEquiv i).source ∩ Z.localTrivAsLocalEquiv i ⁻¹' s}
+    {(Z.localTrivAsPartialEquiv i).source ∩ Z.localTrivAsPartialEquiv i ⁻¹' s}
 #align fiber_bundle_core.to_topological_space FiberBundleCore.toTopologicalSpace
 
 variable (b : B) (a : F)
 
-theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source := by
+theorem open_source' (i : ι) : IsOpen (Z.localTrivAsPartialEquiv i).source := by
   apply TopologicalSpace.GenerateOpen.basic
   simp only [exists_prop, mem_iUnion, mem_singleton_iff]
   refine ⟨i, Z.baseSet i ×ˢ univ, (Z.isOpen_baseSet i).prod isOpen_univ, ?_⟩
   ext p
-  simp only [localTrivAsLocalEquiv_apply, prod_mk_mem_set_prod_eq, mem_inter_iff, and_self_iff,
-    mem_localTrivAsLocalEquiv_source, and_true, mem_univ, mem_preimage]
+  simp only [localTrivAsPartialEquiv_apply, prod_mk_mem_set_prod_eq, mem_inter_iff, and_self_iff,
+    mem_localTrivAsPartialEquiv_source, and_true, mem_univ, mem_preimage]
 #align fiber_bundle_core.open_source' FiberBundleCore.open_source'
 
 /-- Extended version of the local trivialization of a fiber bundle constructed from core,
@@ -582,20 +581,20 @@ def localTriv (i : ι) : Trivialization F Z.proj where
     refine continuousOn_isOpen_of_generateFrom fun t ht ↦ ?_
     simp only [exists_prop, mem_iUnion, mem_singleton_iff] at ht
     obtain ⟨j, s, s_open, ts⟩ : ∃ j s, IsOpen s ∧
-      t = (localTrivAsLocalEquiv Z j).source ∩ localTrivAsLocalEquiv Z j ⁻¹' s := ht
+      t = (localTrivAsPartialEquiv Z j).source ∩ localTrivAsPartialEquiv Z j ⁻¹' s := ht
     rw [ts]
-    simp only [LocalEquiv.right_inv, preimage_inter, LocalEquiv.left_inv]
-    let e := Z.localTrivAsLocalEquiv i
-    let e' := Z.localTrivAsLocalEquiv j
+    simp only [PartialEquiv.right_inv, preimage_inter, PartialEquiv.left_inv]
+    let e := Z.localTrivAsPartialEquiv i
+    let e' := Z.localTrivAsPartialEquiv j
     let f := e.symm.trans e'
     have : IsOpen (f.source ∩ f ⁻¹' s) := by
-      rw [LocalEquiv.EqOnSource.source_inter_preimage_eq (Z.localTrivAsLocalEquiv_trans i j)]
+      rw [PartialEquiv.EqOnSource.source_inter_preimage_eq (Z.localTrivAsPartialEquiv_trans i j)]
       exact (continuousOn_open_iff (Z.trivChange i j).open_source).1
         (Z.trivChange i j).continuousOn _ s_open
     convert this using 1
-    dsimp [LocalEquiv.trans_source]
+    dsimp [PartialEquiv.trans_source]
     rw [← preimage_comp, inter_assoc]
-  toLocalEquiv := Z.localTrivAsLocalEquiv i
+  toPartialEquiv := Z.localTrivAsPartialEquiv i
 #align fiber_bundle_core.local_triv FiberBundleCore.localTriv
 
 /-- Preferred local trivialization of a fiber bundle constructed from core, at a given point, as
@@ -633,27 +632,27 @@ theorem continuous_const_section (v : F)
 #align fiber_bundle_core.continuous_const_section FiberBundleCore.continuous_const_section
 
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_coe : ⇑(Z.localTrivAsLocalEquiv i) = Z.localTriv i :=
+theorem localTrivAsPartialEquiv_coe : ⇑(Z.localTrivAsPartialEquiv i) = Z.localTriv i :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsLocalEquiv_coe
+#align fiber_bundle_core.local_triv_as_local_equiv_coe FiberBundleCore.localTrivAsPartialEquiv_coe
 
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_source :
-    (Z.localTrivAsLocalEquiv i).source = (Z.localTriv i).source :=
+theorem localTrivAsPartialEquiv_source :
+    (Z.localTrivAsPartialEquiv i).source = (Z.localTriv i).source :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsLocalEquiv_source
+#align fiber_bundle_core.local_triv_as_local_equiv_source FiberBundleCore.localTrivAsPartialEquiv_source
 
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_target :
-    (Z.localTrivAsLocalEquiv i).target = (Z.localTriv i).target :=
+theorem localTrivAsPartialEquiv_target :
+    (Z.localTrivAsPartialEquiv i).target = (Z.localTriv i).target :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsLocalEquiv_target
+#align fiber_bundle_core.local_triv_as_local_equiv_target FiberBundleCore.localTrivAsPartialEquiv_target
 
 @[simp, mfld_simps]
-theorem localTrivAsLocalEquiv_symm :
-    (Z.localTrivAsLocalEquiv i).symm = (Z.localTriv i).toLocalEquiv.symm :=
+theorem localTrivAsPartialEquiv_symm :
+    (Z.localTrivAsPartialEquiv i).symm = (Z.localTriv i).toPartialEquiv.symm :=
   rfl
-#align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsLocalEquiv_symm
+#align fiber_bundle_core.local_triv_as_local_equiv_symm FiberBundleCore.localTrivAsPartialEquiv_symm
 
 @[simp, mfld_simps]
 theorem baseSet_at : Z.baseSet i = (Z.localTriv i).baseSet :=
@@ -770,7 +769,7 @@ structure FiberPrebundle where
   mem_base_pretrivializationAt : ∀ x : B, x ∈ (pretrivializationAt x).baseSet
   pretrivialization_mem_atlas : ∀ x : B, pretrivializationAt x ∈ pretrivializationAtlas
   continuous_trivChange : ∀ e, e ∈ pretrivializationAtlas → ∀ e', e' ∈ pretrivializationAtlas →
-    ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
+    ContinuousOn (e ∘ e'.toPartialEquiv.symm) (e'.target ∩ e'.toPartialEquiv.symm ⁻¹' e.source)
   totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivializationAt b ∘ TotalSpace.mk b)
 #align fiber_prebundle FiberPrebundle
 
@@ -786,7 +785,7 @@ def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace F
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
 
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
-    @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target := by
+    @ContinuousOn _ _ _ a.totalSpaceTopology e.toPartialEquiv.symm e.target := by
   refine' fun z H U h => preimage_nhdsWithin_coinduced' H (le_def.1 (nhds_mono _) U h)
   exact le_iSup₂ (α := TopologicalSpace (TotalSpace F E)) e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
@@ -802,7 +801,7 @@ theorem isOpen_source (e : Pretrivialization F (π F E)) :
 
 theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π F E))
     (he' : e' ∈ a.pretrivializationAtlas) :
-    IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) := by
+    IsOpen (e'.toPartialEquiv.target ∩ e'.toPartialEquiv.symm ⁻¹' e.source) := by
   letI := a.totalSpaceTopology
   obtain ⟨u, hu1, hu2⟩ := continuousOn_iff'.mp (a.continuous_symm_of_mem_pretrivializationAtlas he')
     e.source (a.isOpen_source e)
@@ -824,7 +823,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
       obtain ⟨u, hu1, hu2⟩ := continuousOn_iff'.mp (a.continuous_trivChange _ he _ he') s hs
       have hu3 := congr_arg (fun s => (fun x : e'.target => (x : B × F)) ⁻¹' s) hu2
       simp only [Subtype.coe_preimage_self, preimage_inter, univ_inter] at hu3
-      refine ⟨u ∩ e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source, ?_, by
+      refine ⟨u ∩ e'.toPartialEquiv.target ∩ e'.toPartialEquiv.symm ⁻¹' e.source, ?_, by
         simp only [preimage_inter, inter_univ, Subtype.coe_preimage_self, hu3.symm]; rfl⟩
       rw [inter_assoc]
       exact hu1.inter (a.isOpen_target_of_mem_pretrivializationAtlas_inter e e' he')
@@ -900,7 +899,7 @@ continuity of a function `TotalSpace F E → X` on an open set `s` can be checke
 each point with the pretrivialization used for the construction at that point. -/
 theorem continuousOn_of_comp_right {X : Type*} [TopologicalSpace X] {f : TotalSpace F E → X}
     {s : Set B} (hs : IsOpen s) (hf : ∀ b ∈ s,
-      ContinuousOn (f ∘ (a.pretrivializationAt b).toLocalEquiv.symm)
+      ContinuousOn (f ∘ (a.pretrivializationAt b).toPartialEquiv.symm)
         ((s ∩ (a.pretrivializationAt b).baseSet) ×ˢ (Set.univ : Set F))) :
     @ContinuousOn _ _ a.totalSpaceTopology _ f (π F E ⁻¹' s) := by
   letI := a.totalSpaceTopology

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

@@ -444,7 +444,7 @@ def proj : Z.TotalSpace → B :=
 #align fiber_bundle_core.proj FiberBundleCore.proj
 
 /-- Local homeomorphism version of the trivialization change. -/
-def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F) where
+def trivChange (i j : ι) : PartialHomeomorph (B × F) (B × F) where
   source := (Z.baseSet i ∩ Z.baseSet j) ×ˢ univ
   target := (Z.baseSet i ∩ Z.baseSet j) ×ˢ univ
   toFun p := ⟨p.1, Z.coordChange i j p.1 p.2⟩
@@ -623,7 +623,7 @@ theorem continuous_const_section (v : F)
   refine continuous_iff_continuousAt.2 fun x => ?_
   have A : Z.baseSet (Z.indexAt x) ∈ 𝓝 x :=
     IsOpen.mem_nhds (Z.isOpen_baseSet (Z.indexAt x)) (Z.mem_baseSet_at x)
-  refine ((Z.localTrivAt x).toLocalHomeomorph.continuousAt_iff_continuousAt_comp_left ?_).2 ?_
+  refine ((Z.localTrivAt x).toPartialHomeomorph.continuousAt_iff_continuousAt_comp_left ?_).2 ?_
   · exact A
   · apply continuousAt_id.prod
     simp only [(· ∘ ·), mfld_simps, localTrivAt_snd]
@@ -703,7 +703,7 @@ theorem mem_localTrivAt_target (p : B × F) (b : B) :
 
 @[simp, mfld_simps]
 theorem localTriv_symm_apply (p : B × F) :
-    (Z.localTriv i).toLocalHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
+    (Z.localTriv i).toPartialHomeomorph.symm p = ⟨p.1, Z.coordChange i (Z.indexAt p.1) p.1 p.2⟩ :=
   rfl
 #align fiber_bundle_core.local_triv_symm_apply FiberBundleCore.localTriv_symm_apply
 
@@ -848,7 +848,7 @@ theorem continuous_totalSpaceMk (b : B) :
     Continuous[_, a.totalSpaceTopology] (TotalSpace.mk b) := by
   letI := a.totalSpaceTopology
   let e := a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas b)
-  rw [e.toLocalHomeomorph.continuous_iff_continuous_comp_left
+  rw [e.toPartialHomeomorph.continuous_iff_continuous_comp_left
       (a.totalSpaceMk_preimage_source b)]
   exact continuous_iff_le_induced.mpr (le_antisymm_iff.mp (a.totalSpaceMk_inducing b).induced).1
 #align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMk

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

@@ -466,8 +466,8 @@ def trivChange (i j : ι) : LocalHomeomorph (B × F) (B × F) where
     · simp [hx]
   open_source := ((Z.isOpen_baseSet i).inter (Z.isOpen_baseSet j)).prod isOpen_univ
   open_target := ((Z.isOpen_baseSet i).inter (Z.isOpen_baseSet j)).prod isOpen_univ
-  continuous_toFun := continuous_fst.continuousOn.prod (Z.continuousOn_coordChange i j)
-  continuous_invFun := by
+  continuousOn_toFun := continuous_fst.continuousOn.prod (Z.continuousOn_coordChange i j)
+  continuousOn_invFun := by
     simpa [inter_comm] using continuous_fst.continuousOn.prod (Z.continuousOn_coordChange j i)
 #align fiber_bundle_core.triv_change FiberBundleCore.trivChange
 
@@ -572,13 +572,13 @@ def localTriv (i : ι) : Trivialization F Z.proj where
     rfl
   open_source := Z.open_source' i
   open_target := (Z.isOpen_baseSet i).prod isOpen_univ
-  continuous_toFun := by
+  continuousOn_toFun := by
     rw [continuousOn_open_iff (Z.open_source' i)]
     intro s s_open
     apply TopologicalSpace.GenerateOpen.basic
     simp only [exists_prop, mem_iUnion, mem_singleton_iff]
     exact ⟨i, s, s_open, rfl⟩
-  continuous_invFun := by
+  continuousOn_invFun := by
     refine continuousOn_isOpen_of_generateFrom fun t ht ↦ ?_
     simp only [exists_prop, mem_iUnion, mem_singleton_iff] at ht
     obtain ⟨j, s, s_open, ts⟩ : ∃ j s, IsOpen s ∧
@@ -816,7 +816,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
   let _ := a.totalSpaceTopology
   { e with
     open_source := a.isOpen_source e,
-    continuous_toFun := by
+    continuousOn_toFun := by
       refine continuousOn_iff'.mpr fun s hs => ⟨e ⁻¹' s ∩ e.source,
         isOpen_iSup_iff.mpr fun e' => ?_, by rw [inter_assoc, inter_self]; rfl⟩
       refine isOpen_iSup_iff.mpr fun he' => ?_
@@ -828,7 +828,7 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
         simp only [preimage_inter, inter_univ, Subtype.coe_preimage_self, hu3.symm]; rfl⟩
       rw [inter_assoc]
       exact hu1.inter (a.isOpen_target_of_mem_pretrivializationAtlas_inter e e' he')
-    continuous_invFun := a.continuous_symm_of_mem_pretrivializationAtlas he }
+    continuousOn_invFun := a.continuous_symm_of_mem_pretrivializationAtlas he }
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
 
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
@@ -861,7 +861,7 @@ theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
   apply Inducing.of_codRestrict (a.mem_pretrivializationAt_source b)
   refine inducing_of_inducing_compose ?_ (continuousOn_iff_continuous_restrict.mp
     (a.trivializationOfMemPretrivializationAtlas
-      (a.pretrivialization_mem_atlas b)).continuous_toFun) h
+      (a.pretrivialization_mem_atlas b)).continuousOn_toFun) h
   exact (a.continuous_totalSpaceMk b).codRestrict (a.mem_pretrivializationAt_source b)
 #align fiber_prebundle.inducing_total_space_mk_of_inducing_comp FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp
 

Mostly, this means replacing "of_open" by "of_isOpen". A few lemmas names were misleading and are corrected differently. Zulip discussion.

@@ -579,7 +579,7 @@ def localTriv (i : ι) : Trivialization F Z.proj where
     simp only [exists_prop, mem_iUnion, mem_singleton_iff]
     exact ⟨i, s, s_open, rfl⟩
   continuous_invFun := by
-    refine continuousOn_open_of_generateFrom fun t ht ↦ ?_
+    refine continuousOn_isOpen_of_generateFrom fun t ht ↦ ?_
     simp only [exists_prop, mem_iUnion, mem_singleton_iff] at ht
     obtain ⟨j, s, s_open, ts⟩ : ∃ j s, IsOpen s ∧
       t = (localTrivAsLocalEquiv Z j).source ∩ localTrivAsLocalEquiv Z j ⁻¹' s := ht

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

@@ -845,7 +845,7 @@ theorem totalSpaceMk_preimage_source (b : B) :
 
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
-  Continuous[_, a.totalSpaceTopology] (TotalSpace.mk b) := by
+    Continuous[_, a.totalSpaceTopology] (TotalSpace.mk b) := by
   letI := a.totalSpaceTopology
   let e := a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas b)
   rw [e.toLocalHomeomorph.continuous_iff_continuous_comp_left

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

This has nice performance benefits.

@@ -15,7 +15,7 @@ Mathematically, a (topological) fiber bundle with fiber `F` over a base `B` is a
 point is a direct product.
 
 In our formalism, a fiber bundle is by definition the type `Bundle.TotalSpace F E` where
-`E : B → Type _` is a function associating to `x : B` the fiber over `x`. This type
+`E : B → Type*` is a function associating to `x : B` the fiber over `x`. This type
 `Bundle.TotalSpace F E` is a type of pairs `⟨proj : B, snd : E proj⟩`.
 
 To have a fiber bundle structure on `Bundle.TotalSpace F E`, one should
@@ -45,7 +45,7 @@ fiber bundle from trivializations given as local equivalences with minimum addit
 
 ### Basic definitions
 
-* `FiberBundle F E` : Structure saying that `E : B → Type _` is a fiber bundle with fiber `F`.
+* `FiberBundle F E` : Structure saying that `E : B → Type*` is a fiber bundle with fiber `F`.
 
 ### Construction of a bundle from trivializations
 
@@ -164,7 +164,7 @@ Fiber bundle, topological bundle, structure group
 -/
 
 
-variable {ι B F X : Type _} [TopologicalSpace X]
+variable {ι B F X : Type*} [TopologicalSpace X]
 
 open TopologicalSpace Filter Set Bundle Topology
 
@@ -172,7 +172,7 @@ open TopologicalSpace Filter Set Bundle Topology
 
 section FiberBundle
 
-variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
+variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type*)
   [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
@@ -394,7 +394,7 @@ Trivialization changes from `i` to `j` are given by continuous maps `coordChange
 `B → F → F` and require continuity on `(baseSet i ∩ baseSet j) × F` to avoid the topology on the
 space of continuous maps on `F`. -/
 -- porting note: was @[nolint has_nonempty_instance]
-structure FiberBundleCore (ι : Type _) (B : Type _) [TopologicalSpace B] (F : Type _)
+structure FiberBundleCore (ι : Type*) (B : Type*) [TopologicalSpace B] (F : Type*)
     [TopologicalSpace F] where
   baseSet : ι → Set B
   isOpen_baseSet : ∀ i, IsOpen (baseSet i)
@@ -756,7 +756,7 @@ end FiberBundleCore
 
 /-! ### Prebundle construction for constructing fiber bundles -/
 
-variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
+variable (F) (E : B → Type*) [TopologicalSpace B] [TopologicalSpace F]
   [∀ x, TopologicalSpace (E x)]
 
 /-- This structure permits to define a fiber bundle when trivializations are given as local
@@ -898,7 +898,7 @@ instance {e₀} (he₀ : e₀ ∈ a.pretrivializationAtlas) :
 /-- For a fiber bundle `E` over `B` constructed using the `FiberPrebundle` mechanism,
 continuity of a function `TotalSpace F E → X` on an open set `s` can be checked by precomposing at
 each point with the pretrivialization used for the construction at that point. -/
-theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalSpace F E → X}
+theorem continuousOn_of_comp_right {X : Type*} [TopologicalSpace X] {f : TotalSpace F E → X}
     {s : Set B} (hs : IsOpen s) (hf : ∀ b ∈ s,
       ContinuousOn (f ∘ (a.pretrivializationAt b).toLocalEquiv.symm)
         ((s ∩ (a.pretrivializationAt b).baseSet) ×ˢ (Set.univ : Set F))) :

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
-
-! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.FiberBundle.Trivialization
 
+#align_import topology.fiber_bundle.basic from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-!
 # Fiber bundles
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -357,7 +357,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   cases' hc.2.eq_or_lt with heq hlt
   · exact ⟨ec, heq ▸ hec⟩
   suffices : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
-  · rcases this with  ⟨d, hdcb, hd⟩ -- porting note: todo: use `rsuffices`
+  · rcases this with ⟨d, hdcb, hd⟩ -- porting note: todo: use `rsuffices`
     exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
   /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
     `d ∈ (c, b]`. -/

Forward-port leanprover-community/mathlib#19221

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit f7ebde7ee0d1505dfccac8644ae12371aa3c1c9f
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,17 +17,15 @@ Mathematically, a (topological) fiber bundle with fiber `F` over a base `B` is a
 `B` for which the fibers are all homeomorphic to `F`, such that the local situation around each
 point is a direct product.
 
-In our formalism, a fiber bundle is by definition the type
-`Bundle.TotalSpace E` where `E : B → Type*` is a function associating to
-`x : B` the fiber over `x`. This type `Bundle.TotalSpace E` is just a type synonym for
-`Σ (x : B), E x`, with the interest that one can put another topology than on `Σ (x : B), E x`
-which has the disjoint union topology.
+In our formalism, a fiber bundle is by definition the type `Bundle.TotalSpace F E` where
+`E : B → Type _` is a function associating to `x : B` the fiber over `x`. This type
+`Bundle.TotalSpace F E` is a type of pairs `⟨proj : B, snd : E proj⟩`.
 
-To have a fiber bundle structure on `Bundle.TotalSpace E`, one should
+To have a fiber bundle structure on `Bundle.TotalSpace F E`, one should
 additionally have the following data:
 
 * `F` should be a topological space;
-* There should be a topology on `Bundle.TotalSpace E`, for which the projection to `B` is
+* There should be a topology on `Bundle.TotalSpace F E`, for which the projection to `B` is
 a fiber bundle with fiber `F` (in particular, each fiber `E x` is homeomorphic to `F`);
 * For each `x`, the fiber `E x` should be a topological space, and the injection
 from `E x` to `Bundle.TotalSpace F E` should be an embedding;
@@ -54,19 +52,18 @@ fiber bundle from trivializations given as local equivalences with minimum addit
 
 ### Construction of a bundle from trivializations
 
-* `Bundle.TotalSpace E` is a type synonym for `Σ (x : B), E x`, that we can endow with a suitable
-  topology.
+* `Bundle.TotalSpace F E` is the type of pairs `(proj : B, snd : E proj)`. We can use the extra
+  argument `F` to construct topology on the total space.
 * `FiberBundleCore ι B F` : structure registering how changes of coordinates act
   on the fiber `F` above open subsets of `B`, where local trivializations are indexed by `ι`.
 
 Let `Z : FiberBundleCore ι B F`. Then we define
 
 * `Z.Fiber x`     : the fiber above `x`, homeomorphic to `F` (and defeq to `F` as a type).
-* `Z.TotalSpace` : the total space of `Z`, defined as a `Type` as `Σ (b : B), F`, but with a
-  twisted topology coming from the fiber bundle structure. It is (reducibly) the same as
-  `Bundle.TotalSpace Z.Fiber`.
+* `Z.TotalSpace`  : the total space of `Z`, defined as `Bundle.TotalSpace F Z.Fiber` with a custom
+                    topology.
 * `Z.proj`        : projection from `Z.TotalSpace` to `B`. It is continuous.
-* `Z.localTriv i`: for `i : ι`, bundle trivialization above the set `Z.baseSet i`, which is an
+* `Z.localTriv i` : for `i : ι`, bundle trivialization above the set `Z.baseSet i`, which is an
                     open set in `B`.
 
 * `FiberPrebundle F E` : structure registering a cover of prebundle trivializations
@@ -155,8 +152,8 @@ choose for each `x` one specific trivialization around it. We include this choic
 of the `FiberBundleCore`, as it makes some constructions more
 functorial and it is a nice way to say that the trivializations cover the whole space `B`.
 
-With this definition, the type of the fiber bundle space constructed from the core data is just
-`Σ (b : B), F `, but the topology is not the product one, in general.
+With this definition, the type of the fiber bundle space constructed from the core data is
+`Bundle.TotalSpace F (fun b : B ↦ F)`, but the topology is not the product one, in general.
 
 We also take the indexing type (indexing all the trivializations) as a parameter to the fiber bundle
 core: it could always be taken as a subtype of all the maps from open subsets of `B` to continuous
@@ -174,23 +171,20 @@ variable {ι B F X : Type _} [TopologicalSpace X]
 
 open TopologicalSpace Filter Set Bundle Topology
 
-attribute [mfld_simps]
-  totalSpaceMk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul TotalSpace.mk_cast
-
 /-! ### General definition of fiber bundles -/
 
 section FiberBundle
 
 variable (F) [TopologicalSpace B] [TopologicalSpace F] (E : B → Type _)
-  [TopologicalSpace (TotalSpace E)] [∀ b, TopologicalSpace (E b)]
+  [TopologicalSpace (TotalSpace F E)] [∀ b, TopologicalSpace (E b)]
 
 /-- A (topological) fiber bundle with fiber `F` over a base `B` is a space projecting on `B`
 for which the fibers are all homeomorphic to `F`, such that the local situation around each point
 is a direct product. -/
 class FiberBundle where
-  totalSpaceMk_inducing' : ∀ b : B, Inducing (@totalSpaceMk B E b)
-  trivializationAtlas' : Set (Trivialization F (π E))
-  trivializationAt' : B → Trivialization F (π E)
+  totalSpaceMk_inducing' : ∀ b : B, Inducing (@TotalSpace.mk B F E b)
+  trivializationAtlas' : Set (Trivialization F (π F E))
+  trivializationAt' : B → Trivialization F (π F E)
   mem_baseSet_trivializationAt' : ∀ b : B, b ∈ (trivializationAt' b).baseSet
   trivialization_mem_atlas' : ∀ b : B, trivializationAt' b ∈ trivializationAtlas'
 #align fiber_bundle FiberBundle
@@ -199,13 +193,13 @@ namespace FiberBundle
 
 variable [FiberBundle F E] (b : B)
 
-theorem totalSpaceMk_inducing : Inducing (@totalSpaceMk B E b) := totalSpaceMk_inducing' F b
+theorem totalSpaceMk_inducing : Inducing (@TotalSpace.mk B F E b) := totalSpaceMk_inducing' b
 
 /-- Atlas of a fiber bundle. -/
-abbrev trivializationAtlas : Set (Trivialization F (π E)) := trivializationAtlas'
+abbrev trivializationAtlas : Set (Trivialization F (π F E)) := trivializationAtlas'
 
 /-- Trivialization of a fiber bundle at a point. -/
-abbrev trivializationAt : Trivialization F (π E) := trivializationAt' b
+abbrev trivializationAt : Trivialization F (π F E) := trivializationAt' b
 
 theorem mem_baseSet_trivializationAt : b ∈ (trivializationAt F E b).baseSet :=
   mem_baseSet_trivializationAt' b
@@ -226,7 +220,7 @@ bundle.  This is needed because lemmas about the linearity of trivializations or
 functions to `F →L[R] F`, where `F` is the model fiber) of the transition functions are only
 expected to hold for trivializations in the designated atlas. -/
 @[mk_iff memTrivializationAtlas_iff]
-class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π E)) : Prop where
+class MemTrivializationAtlas [FiberBundle F E] (e : Trivialization F (π F E)) : Prop where
   out : e ∈ trivializationAtlas F E
 #align mem_trivialization_atlas MemTrivializationAtlas
 
@@ -238,7 +232,7 @@ namespace FiberBundle
 variable (F)
 variable [FiberBundle F E]
 
-theorem map_proj_nhds (x : TotalSpace E) : map (π E) (𝓝 x) = 𝓝 x.proj :=
+theorem map_proj_nhds (x : TotalSpace F E) : map (π F E) (𝓝 x) = 𝓝 x.proj :=
   (trivializationAt F E x.proj).map_proj_nhds <|
     (trivializationAt F E x.proj).mem_source.2 <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.map_proj_nhds FiberBundle.map_proj_nhds
@@ -247,18 +241,18 @@ variable (E)
 
 /-- The projection from a fiber bundle to its base is continuous. -/
 @[continuity]
-theorem continuous_proj : Continuous (π E) :=
+theorem continuous_proj : Continuous (π F E) :=
   continuous_iff_continuousAt.2 fun x => (map_proj_nhds F x).le
 #align fiber_bundle.continuous_proj FiberBundle.continuous_proj
 
 /-- The projection from a fiber bundle to its base is an open map. -/
-theorem isOpenMap_proj : IsOpenMap (π E) :=
+theorem isOpenMap_proj : IsOpenMap (π F E) :=
   IsOpenMap.of_nhds_le fun x => (map_proj_nhds F x).ge
 #align fiber_bundle.is_open_map_proj FiberBundle.isOpenMap_proj
 
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a surjective
 map. -/
-theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
+theorem surjective_proj [Nonempty F] : Function.Surjective (π F E) := fun b =>
   let ⟨p, _, hpb⟩ :=
     (trivializationAt F E b).proj_surjOn_baseSet (mem_baseSet_trivializationAt F E b)
   ⟨p, hpb⟩
@@ -266,32 +260,33 @@ theorem surjective_proj [Nonempty F] : Function.Surjective (π E) := fun b =>
 
 /-- The projection from a fiber bundle with a nonempty fiber to its base is a quotient
 map. -/
-theorem quotientMap_proj [Nonempty F] : QuotientMap (π E) :=
+theorem quotientMap_proj [Nonempty F] : QuotientMap (π F E) :=
   (isOpenMap_proj F E).to_quotientMap (continuous_proj F E) (surjective_proj F E)
 #align fiber_bundle.quotient_map_proj FiberBundle.quotientMap_proj
 
-theorem continuous_totalSpaceMk (x : B) : Continuous (@totalSpaceMk B E x) :=
+theorem continuous_totalSpaceMk (x : B) : Continuous (@TotalSpace.mk B F E x) :=
   (totalSpaceMk_inducing F E x).continuous
 #align fiber_bundle.continuous_total_space_mk FiberBundle.continuous_totalSpaceMk
 
-theorem totalSpaceMk_embedding (x : B) : Embedding (@totalSpaceMk B E x) :=
-  ⟨totalSpaceMk_inducing F E x, sigma_mk_injective⟩
+theorem totalSpaceMk_embedding (x : B) : Embedding (@TotalSpace.mk B F E x) :=
+  ⟨totalSpaceMk_inducing F E x, TotalSpace.mk_injective x⟩
 
-theorem totalSpaceMk_closedEmbedding [T1Space B] (x : B) : ClosedEmbedding (@totalSpaceMk B E x) :=
+theorem totalSpaceMk_closedEmbedding [T1Space B] (x : B) :
+    ClosedEmbedding (@TotalSpace.mk B F E x) :=
   ⟨totalSpaceMk_embedding F E x, by
-    rw [range_sigmaMk]
+    rw [TotalSpace.range_mk]
     exact isClosed_singleton.preimage <| continuous_proj F E⟩
 
 variable {E F}
 
 @[simp, mfld_simps]
-theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
+theorem mem_trivializationAt_proj_source {x : TotalSpace F E} :
     x ∈ (trivializationAt F E x.proj).source :=
   (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
 
 -- porting note: removed `@[simp, mfld_simps]` because `simp` could already prove this
-theorem trivializationAt_proj_fst {x : TotalSpace E} :
+theorem trivializationAt_proj_fst {x : TotalSpace F E} :
     ((trivializationAt F E x.proj) x).1 = x.proj :=
   Trivialization.coe_fst' _ <| mem_baseSet_trivializationAt F E x.proj
 #align fiber_bundle.trivialization_at_proj_fst FiberBundle.trivializationAt_proj_fst
@@ -301,7 +296,7 @@ variable (F)
 open Trivialization
 
 /-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
-theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
+theorem continuousWithinAt_totalSpace (f : X → TotalSpace F E) {s : Set X} {x₀ : X} :
     ContinuousWithinAt f s x₀ ↔
       ContinuousWithinAt (fun x => (f x).proj) s x₀ ∧
         ContinuousWithinAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) s x₀ :=
@@ -309,7 +304,7 @@ theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀
 #align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
 
 /-- Characterization of continuous functions (at a point) into a fiber bundle. -/
-theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
+theorem continuousAt_totalSpace (f : X → TotalSpace F E) {x₀ : X} :
     ContinuousAt f x₀ ↔
       ContinuousAt (fun x => (f x).proj) x₀ ∧
         ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ :=
@@ -324,15 +319,15 @@ variable (F E)
 then it is trivial over any closed interval. -/
 theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinearOrder B]
     [OrderTopology B] [FiberBundle F E] (a b : B) :
-    ∃ e : Trivialization F (π E), Icc a b ⊆ e.baseSet := by
-  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π E), a ∈ ea.baseSet :=
+    ∃ e : Trivialization F (π F E), Icc a b ⊆ e.baseSet := by
+  obtain ⟨ea, hea⟩ : ∃ ea : Trivialization F (π F E), a ∈ ea.baseSet :=
     ⟨trivializationAt F E a, mem_baseSet_trivializationAt F E a⟩
   -- If `a < b`, then `[a, b] = ∅`, and the statement is trivial
   cases' lt_or_le b a with hab hab
   · exact ⟨ea, by simp [*]⟩
   /- Let `s` be the set of points `x ∈ [a, b]` such that `E` is trivializable over `[a, x]`.
     We need to show that `b ∈ s`. Let `c = Sup s`. We will show that `c ∈ s` and `c = b`. -/
-  set s : Set B := { x ∈ Icc a b | ∃ e : Trivialization F (π E), Icc a x ⊆ e.baseSet }
+  set s : Set B := { x ∈ Icc a b | ∃ e : Trivialization F (π F E), Icc a x ⊆ e.baseSet }
   have ha : a ∈ s := ⟨left_mem_Icc.2 hab, ea, by simp [hea]⟩
   have sne : s.Nonempty := ⟨a, ha⟩
   have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
@@ -340,13 +335,13 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   set c := sSup s
   have hsc : IsLUB s c := isLUB_csSup sne sbd
   have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
-  obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.baseSet⟩ : c ∈ s := by
+  obtain ⟨-, ec : Trivialization F (π F E), hec : Icc a c ⊆ ec.baseSet⟩ : c ∈ s := by
     cases' hc.1.eq_or_lt with heq hlt
     · rwa [← heq]
     refine ⟨hc, ?_⟩
     /- In order to show that `c ∈ s`, consider a trivialization `ec` of `proj` over a neighborhood
       of `c`. Its base set includes `(c', c]` for some `c' ∈ [a, c)`. -/
-    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π E), c ∈ ec.baseSet :=
+    obtain ⟨ec, hc⟩ : ∃ ec : Trivialization F (π F E), c ∈ ec.baseSet :=
       ⟨trivializationAt F E c, mem_baseSet_trivializationAt F E c⟩
     obtain ⟨c', hc', hc'e⟩ : ∃ c' ∈ Ico a c, Ioc c' c ⊆ ec.baseSet :=
       (mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset hlt).1
@@ -361,7 +356,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
     `d ∈ (c, b]`, hence `c` is not an upper bound of `s`. -/
   cases' hc.2.eq_or_lt with heq hlt
   · exact ⟨ec, heq ▸ hec⟩
-  suffices : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π E), Icc a d ⊆ e.baseSet
+  suffices : ∃ d ∈ Ioc c b, ∃ e : Trivialization F (π F E), Icc a d ⊆ e.baseSet
   · rcases this with  ⟨d, hdcb, hd⟩ -- porting note: todo: use `rsuffices`
     exact ((hsc.1 ⟨⟨hc.1.trans hdcb.1.le, hdcb.2⟩, hd⟩).not_lt hdcb.1).elim
   /- Since the base set of `ec` is open, it includes `[c, d)` (hence, `[a, d)`) for some
@@ -374,7 +369,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   · /- If `(c, d) = ∅`, then let `ed` be a trivialization of `proj` over a neighborhood of `d`.
       Then the disjoint union of `ec` restricted to `(-∞, d)` and `ed` restricted to `(c, ∞)` is
       a trivialization over `[a, d]`. -/
-    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π E), d ∈ ed.baseSet :=
+    obtain ⟨ed, hed⟩ : ∃ ed : Trivialization F (π F E), d ∈ ed.baseSet :=
       ⟨trivializationAt F E d, mem_baseSet_trivializationAt F E d⟩
     refine' ⟨d, hdcb,
       (ec.restrOpen (Iio d) isOpen_Iio).disjointUnion (ed.restrOpen (Ioi c) isOpen_Ioi)
@@ -440,10 +435,9 @@ instance topologicalSpaceFiber (x : B) : TopologicalSpace (Z.Fiber x) := ‹_›
 #align fiber_bundle_core.topological_space_fiber FiberBundleCore.topologicalSpaceFiber
 
 /-- The total space of the fiber bundle, as a convenience function for dot notation.
-It is by definition equal to `Bundle.TotalSpace Z.Fiber`, a.k.a. `Σ x, Z.Fiber x` but with a
-different name for typeclass inference. -/
+It is by definition equal to `Bundle.TotalSpace F Z.Fiber`. -/
 @[reducible]
-def TotalSpace := Bundle.TotalSpace Z.Fiber
+def TotalSpace := Bundle.TotalSpace F Z.Fiber
 #align fiber_bundle_core.total_space FiberBundleCore.TotalSpace
 
 /-- The projection from the total space of a fiber bundle core, on its base. -/
@@ -553,7 +547,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
 
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
 that all the local trivialization are continuous. -/
-instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace Z.Fiber) :=
+instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace F Z.Fiber) :=
   TopologicalSpace.generateFrom <| ⋃ (i : ι) (s : Set (B × F)) (_ : IsOpen s),
     {(Z.localTrivAsLocalEquiv i).source ∩ Z.localTrivAsLocalEquiv i ⁻¹' s}
 #align fiber_bundle_core.to_topological_space FiberBundleCore.toTopologicalSpace
@@ -609,7 +603,7 @@ def localTriv (i : ι) : Trivialization F Z.proj where
 
 /-- Preferred local trivialization of a fiber bundle constructed from core, at a given point, as
 a bundle trivialization -/
-def localTrivAt (b : B) : Trivialization F (π Z.Fiber) :=
+def localTrivAt (b : B) : Trivialization F (π F Z.Fiber) :=
   Z.localTriv (Z.indexAt b)
 #align fiber_bundle_core.local_triv_at FiberBundleCore.localTrivAt
 
@@ -698,12 +692,6 @@ theorem mem_localTrivAt_source (p : Z.TotalSpace) (b : B) :
   Iff.rfl
 #align fiber_bundle_core.mem_local_triv_at_source FiberBundleCore.mem_localTrivAt_source
 
-@[simp, mfld_simps]
-theorem mem_source_at : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
-  rw [localTrivAt, mem_localTriv_source]
-  exact Z.mem_baseSet_at b
-#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_source_at
-
 @[simp, mfld_simps]
 theorem mem_localTriv_target (p : B × F) :
     p ∈ (Z.localTriv i).target ↔ p.1 ∈ (Z.localTriv i).baseSet :=
@@ -728,16 +716,21 @@ theorem mem_localTrivAt_baseSet (b : B) : b ∈ (Z.localTrivAt b).baseSet := by
   exact Z.mem_baseSet_at b
 #align fiber_bundle_core.mem_local_triv_at_base_set FiberBundleCore.mem_localTrivAt_baseSet
 
+-- porting note: was @[simp, mfld_simps], now `simp` can prove it
+theorem mk_mem_localTrivAt_source : (⟨b, a⟩ : Z.TotalSpace) ∈ (Z.localTrivAt b).source := by
+  simp only [mfld_simps]
+#align fiber_bundle_core.mem_source_at FiberBundleCore.mem_localTrivAt_source
+
 /-- A fiber bundle constructed from core is indeed a fiber bundle. -/
 instance fiberBundle : FiberBundle F Z.Fiber where
   totalSpaceMk_inducing' b := inducing_iff_nhds.2 fun x ↦ by
-    rw [(Z.localTrivAt b).nhds_eq_comap_inf_principal (mem_source_at _ _ _), comap_inf,
+    rw [(Z.localTrivAt b).nhds_eq_comap_inf_principal (mk_mem_localTrivAt_source _ _ _), comap_inf,
       comap_principal, comap_comap]
-    simp only [(· ∘ ·), totalSpaceMk, localTrivAt_apply_mk, Trivialization.coe_coe,
+    simp only [(· ∘ ·), localTrivAt_apply_mk, Trivialization.coe_coe,
       ← (embedding_prod_mk b).nhds_eq_comap]
     convert_to 𝓝 x = 𝓝 x ⊓ 𝓟 univ
     · congr
-      exact eq_univ_of_forall (mem_source_at Z _)
+      exact eq_univ_of_forall (mk_mem_localTrivAt_source Z _)
     · rw [principal_univ, inf_top_eq]
   trivializationAtlas' := Set.range Z.localTriv
   trivializationAt' := Z.localTrivAt
@@ -748,7 +741,7 @@ instance fiberBundle : FiberBundle F Z.Fiber where
 /-- The inclusion of a fiber into the total space is a continuous map. -/
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
-    Continuous (totalSpaceMk b : Z.Fiber b → Bundle.TotalSpace Z.Fiber) :=
+    Continuous (TotalSpace.mk b : Z.Fiber b → Bundle.TotalSpace F Z.Fiber) :=
   FiberBundle.continuous_totalSpaceMk F Z.Fiber b
 #align fiber_bundle_core.continuous_total_space_mk FiberBundleCore.continuous_totalSpaceMk
 
@@ -775,33 +768,34 @@ topology in such a way that there is a fiber bundle structure for which the loca
 are also local homeomorphism and hence local trivializations. -/
 -- porting note: todo: was @[nolint has_nonempty_instance]
 structure FiberPrebundle where
-  pretrivializationAtlas : Set (Pretrivialization F (π E))
-  pretrivializationAt : B → Pretrivialization F (π E)
+  pretrivializationAtlas : Set (Pretrivialization F (π F E))
+  pretrivializationAt : B → Pretrivialization F (π F E)
   mem_base_pretrivializationAt : ∀ x : B, x ∈ (pretrivializationAt x).baseSet
   pretrivialization_mem_atlas : ∀ x : B, pretrivializationAt x ∈ pretrivializationAtlas
   continuous_trivChange : ∀ e, e ∈ pretrivializationAtlas → ∀ e', e' ∈ pretrivializationAtlas →
     ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
-  totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivializationAt b ∘ totalSpaceMk b)
+  totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivializationAt b ∘ TotalSpace.mk b)
 #align fiber_prebundle FiberPrebundle
 
 namespace FiberPrebundle
 
 variable {F E}
-variable (a : FiberPrebundle F E) {e : Pretrivialization F (π E)}
+variable (a : FiberPrebundle F E) {e : Pretrivialization F (π F E)}
 
 /-- Topology on the total space that will make the prebundle into a bundle. -/
-def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E) :=
-  ⨆ (e : Pretrivialization F (π E)) (_ : e ∈ a.pretrivializationAtlas),
+def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace F E) :=
+  ⨆ (e : Pretrivialization F (π F E)) (_ : e ∈ a.pretrivializationAtlas),
     coinduced e.setSymm instTopologicalSpaceSubtype
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
 
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target := by
   refine' fun z H U h => preimage_nhdsWithin_coinduced' H (le_def.1 (nhds_mono _) U h)
-  exact le_iSup₂ (α := TopologicalSpace (TotalSpace E)) e he
+  exact le_iSup₂ (α := TopologicalSpace (TotalSpace F E)) e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
 
-theorem isOpen_source (e : Pretrivialization F (π E)) : IsOpen[a.totalSpaceTopology] e.source := by
+theorem isOpen_source (e : Pretrivialization F (π F E)) :
+    IsOpen[a.totalSpaceTopology] e.source := by
   refine isOpen_iSup_iff.mpr fun e' => isOpen_iSup_iff.mpr fun _ => ?_
   refine' isOpen_coinduced.mpr (isOpen_induced_iff.mpr ⟨e.target, e.open_target, _⟩)
   ext ⟨x, hx⟩
@@ -809,7 +803,7 @@ theorem isOpen_source (e : Pretrivialization F (π E)) : IsOpen[a.totalSpaceTopo
     e'.proj_symm_apply hx]
 #align fiber_prebundle.is_open_source FiberPrebundle.isOpen_source
 
-theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π E))
+theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivialization F (π F E))
     (he' : e' ∈ a.pretrivializationAtlas) :
     IsOpen (e'.toLocalEquiv.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source) := by
   letI := a.totalSpaceTopology
@@ -821,7 +815,7 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
 
 /-- Promotion from a `Pretrivialization` to a `Trivialization`. -/
 def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
-    @Trivialization B F _ _ _ a.totalSpaceTopology (π E) :=
+    @Trivialization B F _ _ _ a.totalSpaceTopology (π F E) :=
   let _ := a.totalSpaceTopology
   { e with
     open_source := a.isOpen_source e,
@@ -841,20 +835,20 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
 #align fiber_prebundle.trivialization_of_mem_pretrivialization_atlas FiberPrebundle.trivializationOfMemPretrivializationAtlas
 
 theorem mem_pretrivializationAt_source (b : B) (x : E b) :
-    totalSpaceMk b x ∈ (a.pretrivializationAt b).source := by
+    ⟨b, x⟩ ∈ (a.pretrivializationAt b).source := by
   simp only [(a.pretrivializationAt b).source_eq, mem_preimage, TotalSpace.proj]
   exact a.mem_base_pretrivializationAt b
 #align fiber_prebundle.mem_trivialization_at_source FiberPrebundle.mem_pretrivializationAt_source
 
 @[simp]
 theorem totalSpaceMk_preimage_source (b : B) :
-    totalSpaceMk b ⁻¹' (a.pretrivializationAt b).source = univ :=
+    TotalSpace.mk b ⁻¹' (a.pretrivializationAt b).source = univ :=
   eq_univ_of_forall (a.mem_pretrivializationAt_source b)
 #align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_source
 
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
-  Continuous[_, a.totalSpaceTopology] (totalSpaceMk b) := by
+  Continuous[_, a.totalSpaceTopology] (TotalSpace.mk b) := by
   letI := a.totalSpaceTopology
   let e := a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas b)
   rw [e.toLocalHomeomorph.continuous_iff_continuous_comp_left
@@ -863,8 +857,8 @@ theorem continuous_totalSpaceMk (b : B) :
 #align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMk
 
 theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
-    (h : Inducing (a.pretrivializationAt b ∘ totalSpaceMk b)) :
-    @Inducing _ _ _ a.totalSpaceTopology (totalSpaceMk b) := by
+    (h : Inducing (a.pretrivializationAt b ∘ TotalSpace.mk b)) :
+    @Inducing _ _ _ a.totalSpaceTopology (TotalSpace.mk b) := by
   letI := a.totalSpaceTopology
   rw [← restrict_comp_codRestrict (a.mem_pretrivializationAt_source b)] at h
   apply Inducing.of_codRestrict (a.mem_pretrivializationAt_source b)
@@ -893,7 +887,7 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _ :=
     trivialization_mem_atlas' := fun x ↦ ⟨_, a.pretrivialization_mem_atlas x, rfl⟩ }
 #align fiber_prebundle.to_fiber_bundle FiberPrebundle.toFiberBundle
 
-theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) := by
+theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π F E) := by
   letI := a.totalSpaceTopology
   letI := a.toFiberBundle
   exact FiberBundle.continuous_proj F E
@@ -905,16 +899,16 @@ instance {e₀} (he₀ : e₀ ∈ a.pretrivializationAtlas) :
   letI := a.totalSpaceTopology; letI := a.toFiberBundle; ⟨e₀, he₀, rfl⟩
 
 /-- For a fiber bundle `E` over `B` constructed using the `FiberPrebundle` mechanism,
-continuity of a function `TotalSpace E → X` on an open set `s` can be checked by precomposing at
+continuity of a function `TotalSpace F E → X` on an open set `s` can be checked by precomposing at
 each point with the pretrivialization used for the construction at that point. -/
-theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalSpace E → X}
+theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalSpace F E → X}
     {s : Set B} (hs : IsOpen s) (hf : ∀ b ∈ s,
       ContinuousOn (f ∘ (a.pretrivializationAt b).toLocalEquiv.symm)
         ((s ∩ (a.pretrivializationAt b).baseSet) ×ˢ (Set.univ : Set F))) :
-    @ContinuousOn _ _ a.totalSpaceTopology _ f (π E ⁻¹' s) := by
+    @ContinuousOn _ _ a.totalSpaceTopology _ f (π F E ⁻¹' s) := by
   letI := a.totalSpaceTopology
   intro z hz
-  let e : Trivialization F (π E) :=
+  let e : Trivialization F (π F E) :=
     a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas z.proj)
   refine' (e.continuousAt_of_comp_right _
     ((hf z.proj hz).continuousAt (IsOpen.mem_nhds _ _))).continuousWithinAt

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

@@ -304,28 +304,16 @@ open Trivialization
 theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
     ContinuousWithinAt f s x₀ ↔
       ContinuousWithinAt (fun x => (f x).proj) s x₀ ∧
-        ContinuousWithinAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) s x₀ := by
-  refine' (and_iff_right_iff_imp.2 fun hf => _).symm.trans (and_congr_right fun hf => _)
-  · refine' (continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s)
-  have h1 : (fun x => (f x).proj) ⁻¹' (trivializationAt F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
-    hf.preimage_mem_nhdsWithin ((open_baseSet _).mem_nhds (mem_baseSet_trivializationAt F E _))
-  have h2 : ContinuousWithinAt (fun x => (trivializationAt F E (f x₀).proj (f x)).1) s x₀ := by
-    refine'
-      hf.congr_of_eventuallyEq (eventually_of_mem h1 fun x hx => _) trivializationAt_proj_fst
-    simp_rw [coe_fst' _ hx]
-  rw [(trivializationAt F E (f x₀).proj).continuousWithinAt_iff_continuousWithinAt_comp_left]
-  · simp_rw [continuousWithinAt_prod_iff, Function.comp, Trivialization.coe_coe, h2, true_and_iff]
-  · apply mem_trivializationAt_proj_source
-  · rwa [source_eq, preimage_preimage]
+        ContinuousWithinAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) s x₀ :=
+  (trivializationAt F E (f x₀).proj).tendsto_nhds_iff mem_trivializationAt_proj_source
 #align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
 
 /-- Characterization of continuous functions (at a point) into a fiber bundle. -/
 theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
     ContinuousAt f x₀ ↔
       ContinuousAt (fun x => (f x).proj) x₀ ∧
-        ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ := by
-  simp_rw [← continuousWithinAt_univ]
-  exact continuousWithinAt_totalSpace F f
+        ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ :=
+  (trivializationAt F E (f x₀).proj).tendsto_nhds_iff mem_trivializationAt_proj_source
 #align fiber_bundle.continuous_at_total_space FiberBundle.continuousAt_totalSpace
 
 end FiberBundle

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -923,7 +923,7 @@ theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalS
     {s : Set B} (hs : IsOpen s) (hf : ∀ b ∈ s,
       ContinuousOn (f ∘ (a.pretrivializationAt b).toLocalEquiv.symm)
         ((s ∩ (a.pretrivializationAt b).baseSet) ×ˢ (Set.univ : Set F))) :
-    @ContinuousOn _ _ a.totalSpaceTopology _ f ((π E) ⁻¹' s) := by
+    @ContinuousOn _ _ a.totalSpaceTopology _ f (π E ⁻¹' s) := by
   letI := a.totalSpaceTopology
   intro z hz
   let e : Trivialization F (π E) :=

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

@@ -911,6 +911,11 @@ theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) := by
   exact FiberBundle.continuous_proj F E
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj
 
+instance {e₀} (he₀ : e₀ ∈ a.pretrivializationAtlas) :
+    (letI := a.totalSpaceTopology; letI := a.toFiberBundle;
+      MemTrivializationAtlas (a.trivializationOfMemPretrivializationAtlas he₀)) :=
+  letI := a.totalSpaceTopology; letI := a.toFiberBundle; ⟨e₀, he₀, rfl⟩
+
 /-- For a fiber bundle `E` over `B` constructed using the `FiberPrebundle` mechanism,
 continuity of a function `TotalSpace E → X` on an open set `s` can be checked by precomposing at
 each point with the pretrivialization used for the construction at that point. -/

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -396,7 +396,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
           `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
     rw [disjoint_left] at he
-    push_neg  at he
+    push_neg at he
     rcases he with ⟨d', hdd' : d' < d, hd'c⟩
     exact ⟨d', ⟨hd'c, hdd'.le.trans hdcb.2⟩, ec, (Icc_subset_Ico_right hdd').trans had⟩
 #align fiber_bundle.exists_trivialization_Icc_subset FiberBundle.exists_trivialization_Icc_subset

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -392,7 +392,7 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
       (ec.restrOpen (Iio d) isOpen_Iio).disjointUnion (ed.restrOpen (Ioi c) isOpen_Ioi)
         (he.mono (inter_subset_right _ _) (inter_subset_right _ _)), fun x hx => _⟩
     rcases hx.2.eq_or_lt with (rfl | hxd)
-    exacts[Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
+    exacts [Or.inr ⟨hed, hdcb.1⟩, Or.inl ⟨had ⟨hx.1, hxd⟩, hxd⟩]
   · /- If `(c, d)` is nonempty, then take `d' ∈ (c, d)`. Since the base set of `ec` includes
           `[a, d)`, it includes `[a, d'] ⊆ [a, d)` as well. -/
     rw [disjoint_left] at he

@@ -566,7 +566,7 @@ theorem localTrivAsLocalEquiv_trans (i j : ι) :
 /-- Topological structure on the total space of a fiber bundle created from core, designed so
 that all the local trivialization are continuous. -/
 instance toTopologicalSpace : TopologicalSpace (Bundle.TotalSpace Z.Fiber) :=
-  TopologicalSpace.generateFrom <| ⋃ (i : ι) (s : Set (B × F)) (_s_open : IsOpen s),
+  TopologicalSpace.generateFrom <| ⋃ (i : ι) (s : Set (B × F)) (_ : IsOpen s),
     {(Z.localTrivAsLocalEquiv i).source ∩ Z.localTrivAsLocalEquiv i ⁻¹' s}
 #align fiber_bundle_core.to_topological_space FiberBundleCore.toTopologicalSpace
 
@@ -803,7 +803,7 @@ variable (a : FiberPrebundle F E) {e : Pretrivialization F (π E)}
 
 /-- Topology on the total space that will make the prebundle into a bundle. -/
 def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E) :=
-  ⨆ (e : Pretrivialization F (π E)) (_he : e ∈ a.pretrivializationAtlas),
+  ⨆ (e : Pretrivialization F (π E)) (_ : e ∈ a.pretrivializationAtlas),
     coinduced e.setSymm instTopologicalSpaceSubtype
 #align fiber_prebundle.total_space_topology FiberPrebundle.totalSpaceTopology
 

Forward-port leanprover-community/mathlib#19107

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit 0187644979f2d3e10a06e916a869c994facd9a87
+! leanprover-community/mathlib commit f7ebde7ee0d1505dfccac8644ae12371aa3c1c9f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -779,6 +779,7 @@ end FiberBundleCore
 /-! ### Prebundle construction for constructing fiber bundles -/
 
 variable (F) (E : B → Type _) [TopologicalSpace B] [TopologicalSpace F]
+  [∀ x, TopologicalSpace (E x)]
 
 /-- This structure permits to define a fiber bundle when trivializations are given as local
 equivalences but there is not yet a topology on the total space. The total space is hence given a
@@ -792,6 +793,7 @@ structure FiberPrebundle where
   pretrivialization_mem_atlas : ∀ x : B, pretrivializationAt x ∈ pretrivializationAtlas
   continuous_trivChange : ∀ e, e ∈ pretrivializationAtlas → ∀ e', e' ∈ pretrivializationAtlas →
     ContinuousOn (e ∘ e'.toLocalEquiv.symm) (e'.target ∩ e'.toLocalEquiv.symm ⁻¹' e.source)
+  totalSpaceMk_inducing : ∀ b : B, Inducing (pretrivializationAt b ∘ totalSpaceMk b)
 #align fiber_prebundle FiberPrebundle
 
 namespace FiberPrebundle
@@ -862,35 +864,38 @@ theorem totalSpaceMk_preimage_source (b : B) :
   eq_univ_of_forall (a.mem_pretrivializationAt_source b)
 #align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_source
 
-/-- Topology on the fibers `E b` induced by the map `E b → E.TotalSpace`. -/
-def fiberTopology (b : B) : TopologicalSpace (E b) :=
-  TopologicalSpace.induced (totalSpaceMk b) a.totalSpaceTopology
-#align fiber_prebundle.fiber_topology FiberPrebundle.fiberTopology
-
-@[continuity]
-theorem inducing_totalSpaceMk (b : B) :
-    @Inducing _ _ (a.fiberTopology b) a.totalSpaceTopology (totalSpaceMk b) := by
-  letI := a.totalSpaceTopology
-  letI := a.fiberTopology b
-  exact ⟨rfl⟩
-#align fiber_prebundle.inducing_total_space_mk FiberPrebundle.inducing_totalSpaceMk
-
 @[continuity]
 theorem continuous_totalSpaceMk (b : B) :
-    Continuous[a.fiberTopology b, a.totalSpaceTopology] (totalSpaceMk b) := by
-  letI := a.totalSpaceTopology; letI := a.fiberTopology b
-  exact (a.inducing_totalSpaceMk b).continuous
+  Continuous[_, a.totalSpaceTopology] (totalSpaceMk b) := by
+  letI := a.totalSpaceTopology
+  let e := a.trivializationOfMemPretrivializationAtlas (a.pretrivialization_mem_atlas b)
+  rw [e.toLocalHomeomorph.continuous_iff_continuous_comp_left
+      (a.totalSpaceMk_preimage_source b)]
+  exact continuous_iff_le_induced.mpr (le_antisymm_iff.mp (a.totalSpaceMk_inducing b).induced).1
 #align fiber_prebundle.continuous_total_space_mk FiberPrebundle.continuous_totalSpaceMk
 
+theorem inducing_totalSpaceMk_of_inducing_comp (b : B)
+    (h : Inducing (a.pretrivializationAt b ∘ totalSpaceMk b)) :
+    @Inducing _ _ _ a.totalSpaceTopology (totalSpaceMk b) := by
+  letI := a.totalSpaceTopology
+  rw [← restrict_comp_codRestrict (a.mem_pretrivializationAt_source b)] at h
+  apply Inducing.of_codRestrict (a.mem_pretrivializationAt_source b)
+  refine inducing_of_inducing_compose ?_ (continuousOn_iff_continuous_restrict.mp
+    (a.trivializationOfMemPretrivializationAtlas
+      (a.pretrivialization_mem_atlas b)).continuous_toFun) h
+  exact (a.continuous_totalSpaceMk b).codRestrict (a.mem_pretrivializationAt_source b)
+#align fiber_prebundle.inducing_total_space_mk_of_inducing_comp FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp
+
 /-- Make a `FiberBundle` from a `FiberPrebundle`.  Concretely this means
 that, given a `FiberPrebundle` structure for a sigma-type `E` -- which consists of a
 number of "pretrivializations" identifying parts of `E` with product spaces `U × F` -- one
 establishes that for the topology constructed on the sigma-type using
 `FiberPrebundle.totalSpaceTopology`, these "pretrivializations" are actually
 "trivializations" (i.e., homeomorphisms with respect to the constructed topology). -/
-def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology :=
-  let _ := a.totalSpaceTopology; let _ := a.fiberTopology
-  { totalSpaceMk_inducing' := a.inducing_totalSpaceMk,
+def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology _ :=
+  let _ := a.totalSpaceTopology
+  { totalSpaceMk_inducing' := fun b ↦ a.inducing_totalSpaceMk_of_inducing_comp b
+      (a.totalSpaceMk_inducing b)
     trivializationAtlas' :=
       { e | ∃ (e₀ : _) (he₀ : e₀ ∈ a.pretrivializationAtlas),
         e = a.trivializationOfMemPretrivializationAtlas he₀ },
@@ -902,7 +907,6 @@ def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology
 
 theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) := by
   letI := a.totalSpaceTopology
-  letI := a.fiberTopology
   letI := a.toFiberBundle
   exact FiberBundle.continuous_proj F E
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

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

@@ -349,8 +349,8 @@ theorem FiberBundle.exists_trivialization_Icc_subset [ConditionallyCompleteLinea
   have sne : s.Nonempty := ⟨a, ha⟩
   have hsb : b ∈ upperBounds s := fun x hx => hx.1.2
   have sbd : BddAbove s := ⟨b, hsb⟩
-  set c := supₛ s
-  have hsc : IsLUB s c := isLUB_csupₛ sne sbd
+  set c := sSup s
+  have hsc : IsLUB s c := isLUB_csSup sne sbd
   have hc : c ∈ Icc a b := ⟨hsc.1 ha, hsc.2 hsb⟩
   obtain ⟨-, ec : Trivialization F (π E), hec : Icc a c ⊆ ec.baseSet⟩ : c ∈ s := by
     cases' hc.1.eq_or_lt with heq hlt
@@ -574,7 +574,7 @@ variable (b : B) (a : F)
 
 theorem open_source' (i : ι) : IsOpen (Z.localTrivAsLocalEquiv i).source := by
   apply TopologicalSpace.GenerateOpen.basic
-  simp only [exists_prop, mem_unionᵢ, mem_singleton_iff]
+  simp only [exists_prop, mem_iUnion, mem_singleton_iff]
   refine ⟨i, Z.baseSet i ×ˢ univ, (Z.isOpen_baseSet i).prod isOpen_univ, ?_⟩
   ext p
   simp only [localTrivAsLocalEquiv_apply, prod_mk_mem_set_prod_eq, mem_inter_iff, and_self_iff,
@@ -597,11 +597,11 @@ def localTriv (i : ι) : Trivialization F Z.proj where
     rw [continuousOn_open_iff (Z.open_source' i)]
     intro s s_open
     apply TopologicalSpace.GenerateOpen.basic
-    simp only [exists_prop, mem_unionᵢ, mem_singleton_iff]
+    simp only [exists_prop, mem_iUnion, mem_singleton_iff]
     exact ⟨i, s, s_open, rfl⟩
   continuous_invFun := by
     refine continuousOn_open_of_generateFrom fun t ht ↦ ?_
-    simp only [exists_prop, mem_unionᵢ, mem_singleton_iff] at ht
+    simp only [exists_prop, mem_iUnion, mem_singleton_iff] at ht
     obtain ⟨j, s, s_open, ts⟩ : ∃ j s, IsOpen s ∧
       t = (localTrivAsLocalEquiv Z j).source ∩ localTrivAsLocalEquiv Z j ⁻¹' s := ht
     rw [ts]
@@ -808,11 +808,11 @@ def totalSpaceTopology (a : FiberPrebundle F E) : TopologicalSpace (TotalSpace E
 theorem continuous_symm_of_mem_pretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @ContinuousOn _ _ _ a.totalSpaceTopology e.toLocalEquiv.symm e.target := by
   refine' fun z H U h => preimage_nhdsWithin_coinduced' H (le_def.1 (nhds_mono _) U h)
-  exact le_supᵢ₂ (α := TopologicalSpace (TotalSpace E)) e he
+  exact le_iSup₂ (α := TopologicalSpace (TotalSpace E)) e he
 #align fiber_prebundle.continuous_symm_of_mem_pretrivialization_atlas FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas
 
 theorem isOpen_source (e : Pretrivialization F (π E)) : IsOpen[a.totalSpaceTopology] e.source := by
-  refine isOpen_supᵢ_iff.mpr fun e' => isOpen_supᵢ_iff.mpr fun _ => ?_
+  refine isOpen_iSup_iff.mpr fun e' => isOpen_iSup_iff.mpr fun _ => ?_
   refine' isOpen_coinduced.mpr (isOpen_induced_iff.mpr ⟨e.target, e.open_target, _⟩)
   ext ⟨x, hx⟩
   simp only [mem_preimage, Pretrivialization.setSymm, restrict, e.mem_target, e.mem_source,
@@ -837,8 +837,8 @@ def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtl
     open_source := a.isOpen_source e,
     continuous_toFun := by
       refine continuousOn_iff'.mpr fun s hs => ⟨e ⁻¹' s ∩ e.source,
-        isOpen_supᵢ_iff.mpr fun e' => ?_, by rw [inter_assoc, inter_self]; rfl⟩
-      refine isOpen_supᵢ_iff.mpr fun he' => ?_
+        isOpen_iSup_iff.mpr fun e' => ?_, by rw [inter_assoc, inter_self]; rfl⟩
+      refine isOpen_iSup_iff.mpr fun he' => ?_
       rw [isOpen_coinduced, isOpen_induced_iff]
       obtain ⟨u, hu1, hu2⟩ := continuousOn_iff'.mp (a.continuous_trivChange _ he _ he') s hs
       have hu3 := congr_arg (fun s => (fun x : e'.target => (x : B × F)) ⁻¹' s) hu2

• leanprover-community/mathlib#18601
• https://leanprover-community.github.io/mathlib-port-status/file/topology/fiber_bundle/basic

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.fiber_bundle.basic
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit 0187644979f2d3e10a06e916a869c994facd9a87
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -170,12 +170,12 @@ Fiber bundle, topological bundle, structure group
 -/
 
 
-variable {ι : Type _} {B : Type _} {F : Type _}
+variable {ι B F X : Type _} [TopologicalSpace X]
 
 open TopologicalSpace Filter Set Bundle Topology
 
 attribute [mfld_simps]
-  TotalSpace.proj totalSpaceMk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul TotalSpace.mk_cast
+  totalSpaceMk coe_fst coe_snd coe_snd_map_apply coe_snd_map_smul TotalSpace.mk_cast
 
 /-! ### General definition of fiber bundles -/
 
@@ -282,6 +282,52 @@ theorem totalSpaceMk_closedEmbedding [T1Space B] (x : B) : ClosedEmbedding (@tot
     rw [range_sigmaMk]
     exact isClosed_singleton.preimage <| continuous_proj F E⟩
 
+variable {E F}
+
+@[simp, mfld_simps]
+theorem mem_trivializationAt_proj_source {x : TotalSpace E} :
+    x ∈ (trivializationAt F E x.proj).source :=
+  (Trivialization.mem_source _).mpr <| mem_baseSet_trivializationAt F E x.proj
+#align fiber_bundle.mem_trivialization_at_proj_source FiberBundle.mem_trivializationAt_proj_source
+
+-- porting note: removed `@[simp, mfld_simps]` because `simp` could already prove this
+theorem trivializationAt_proj_fst {x : TotalSpace E} :
+    ((trivializationAt F E x.proj) x).1 = x.proj :=
+  Trivialization.coe_fst' _ <| mem_baseSet_trivializationAt F E x.proj
+#align fiber_bundle.trivialization_at_proj_fst FiberBundle.trivializationAt_proj_fst
+
+variable (F)
+
+open Trivialization
+
+/-- Characterization of continuous functions (at a point, within a set) into a fiber bundle. -/
+theorem continuousWithinAt_totalSpace (f : X → TotalSpace E) {s : Set X} {x₀ : X} :
+    ContinuousWithinAt f s x₀ ↔
+      ContinuousWithinAt (fun x => (f x).proj) s x₀ ∧
+        ContinuousWithinAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) s x₀ := by
+  refine' (and_iff_right_iff_imp.2 fun hf => _).symm.trans (and_congr_right fun hf => _)
+  · refine' (continuous_proj F E).continuousWithinAt.comp hf (mapsTo_image f s)
+  have h1 : (fun x => (f x).proj) ⁻¹' (trivializationAt F E (f x₀).proj).baseSet ∈ 𝓝[s] x₀ :=
+    hf.preimage_mem_nhdsWithin ((open_baseSet _).mem_nhds (mem_baseSet_trivializationAt F E _))
+  have h2 : ContinuousWithinAt (fun x => (trivializationAt F E (f x₀).proj (f x)).1) s x₀ := by
+    refine'
+      hf.congr_of_eventuallyEq (eventually_of_mem h1 fun x hx => _) trivializationAt_proj_fst
+    simp_rw [coe_fst' _ hx]
+  rw [(trivializationAt F E (f x₀).proj).continuousWithinAt_iff_continuousWithinAt_comp_left]
+  · simp_rw [continuousWithinAt_prod_iff, Function.comp, Trivialization.coe_coe, h2, true_and_iff]
+  · apply mem_trivializationAt_proj_source
+  · rwa [source_eq, preimage_preimage]
+#align fiber_bundle.continuous_within_at_total_space FiberBundle.continuousWithinAt_totalSpace
+
+/-- Characterization of continuous functions (at a point) into a fiber bundle. -/
+theorem continuousAt_totalSpace (f : X → TotalSpace E) {x₀ : X} :
+    ContinuousAt f x₀ ↔
+      ContinuousAt (fun x => (f x).proj) x₀ ∧
+        ContinuousAt (fun x => ((trivializationAt F E (f x₀).proj) (f x)).2) x₀ := by
+  simp_rw [← continuousWithinAt_univ]
+  exact continuousWithinAt_totalSpace F f
+#align fiber_bundle.continuous_at_total_space FiberBundle.continuousAt_totalSpace
+
 end FiberBundle
 
 variable (F E)

@@ -50,7 +50,7 @@ fiber bundle from trivializations given as local equivalences with minimum addit
 
 ### Basic definitions
 
-* `FiberBundle F E` : Structure saying that `E : B → Type*` is a fiber bundle with fiber `F`.
+* `FiberBundle F E` : Structure saying that `E : B → Type _` is a fiber bundle with fiber `F`.
 
 ### Construction of a bundle from trivializations
 
@@ -91,15 +91,15 @@ a family of trivializations (constituting the data) which are all mutually-compa
 The PRs #13052 and #13175 implemented this change.
 
 There is still the choice about whether to hold this data at the level of fiber bundles or of vector
-bundles. As of PR #17505, the data is all held in `FiberBundle`, with `vector_bundle` a
+bundles. As of PR #17505, the data is all held in `FiberBundle`, with `VectorBundle` a
 (propositional) mixin stating fiberwise-linearity.
 
 This allows bundles to carry instances of typeclasses in which the scalar field, `R`, does not
 appear as a parameter. Notably, we would like a vector bundle over `R` with fiber `F` over base `B`
-to be a `charted_space (B × F)`, with the trivializations providing the charts. This would be a
+to be a `ChartedSpace (B × F)`, with the trivializations providing the charts. This would be a
 dangerous instance for typeclass inference, because `R` does not appear as a parameter in
-`charted_space (B × F)`. But if the data of the trivializations is held in `FiberBundle`, then a
-fiber bundle with fiber `F` over base `B` can be a `charted_space (B × F)`, and this is safe for
+`ChartedSpace (B × F)`. But if the data of the trivializations is held in `FiberBundle`, then a
+fiber bundle with fiber `F` over base `B` can be a `ChartedSpace (B × F)`, and this is safe for
 typeclass inference.
 
 We expect that this choice of definition will also streamline constructions of fiber bundles with
@@ -135,7 +135,7 @@ This has several practical advantages:
 * without any work, one gets a topological space structure on the fiber. And if `F` has more
 structure it is inherited for free by the fiber.
 * In the case of the tangent bundle of manifolds, this implies that on vector spaces the derivative
-(from `F` to `F`) and the manifold derivative (from `tangent_space I x` to `tangent_space I' (f x)`)
+(from `F` to `F`) and the manifold derivative (from `TangentSpace I x` to `TangentSpace I' (f x)`)
 are equal.
 
 A drawback is that some silly constructions will typecheck: in the case of the tangent bundle, one
@@ -145,8 +145,8 @@ lose the identification of the tangent space to `F` with `F`. There is however a
 this situation: even if Lean can not check that two basepoints are defeq, it will accept the fact
 that the tangent spaces are the same. For instance, if two maps `f` and `g` are locally inverse to
 each other, one can express that the composition of their derivatives is the identity of
-`tangent_space I x`. One could fear issues as this composition goes from `tangent_space I x` to
-`tangent_space I (g (f x))` (which should be the same, but should not be obvious to Lean
+`TangentSpace I x`. One could fear issues as this composition goes from `TangentSpace I x` to
+`TangentSpace I (g (f x))` (which should be the same, but should not be obvious to Lean
 as it does not know that `g (f x) = x`). As these types are the same to Lean (equal to `F`), there
 are in fact no dependent type difficulties here!
 
@@ -363,7 +363,7 @@ end FiberBundle
 space `B`. Note that "bundle" is used in its mathematical sense. This is the (computer science)
 bundled version, i.e., all the relevant data is contained in the following structure. A family of
 local trivializations is indexed by a type `ι`, on open subsets `baseSet i` for each `i : ι`.
-Trivialization changes from `i` to `j` are given by continuous maps `coord_change i j` from
+Trivialization changes from `i` to `j` are given by continuous maps `coordChange i j` from
 `baseSet i ∩ baseSet j` to the set of homeomorphisms of `F`, but we express them as maps
 `B → F → F` and require continuity on `(baseSet i ∩ baseSet j) × F` to avoid the topology on the
 space of continuous maps on `F`. -/
@@ -786,7 +786,7 @@ theorem isOpen_target_of_mem_pretrivializationAtlas_inter (e e' : Pretrivializat
 /-- Promotion from a `Pretrivialization` to a `Trivialization`. -/
 def trivializationOfMemPretrivializationAtlas (he : e ∈ a.pretrivializationAtlas) :
     @Trivialization B F _ _ _ a.totalSpaceTopology (π E) :=
-  let _ := a.totalSpaceTopology;
+  let _ := a.totalSpaceTopology
   { e with
     open_source := a.isOpen_source e,
     continuous_toFun := by
@@ -816,7 +816,7 @@ theorem totalSpaceMk_preimage_source (b : B) :
   eq_univ_of_forall (a.mem_pretrivializationAt_source b)
 #align fiber_prebundle.total_space_mk_preimage_source FiberPrebundle.totalSpaceMk_preimage_source
 
-/-- Topology on the fibers `E b` induced by the map `E b → E.total_space`. -/
+/-- Topology on the fibers `E b` induced by the map `E b → E.TotalSpace`. -/
 def fiberTopology (b : B) : TopologicalSpace (E b) :=
   TopologicalSpace.induced (totalSpaceMk b) a.totalSpaceTopology
 #align fiber_prebundle.fiber_topology FiberPrebundle.fiberTopology
@@ -843,7 +843,7 @@ establishes that for the topology constructed on the sigma-type using
 `FiberPrebundle.totalSpaceTopology`, these "pretrivializations" are actually
 "trivializations" (i.e., homeomorphisms with respect to the constructed topology). -/
 def toFiberBundle : @FiberBundle B F _ _ E a.totalSpaceTopology a.fiberTopology :=
-  let _ := a.totalSpaceTopology; let _ := a.fiberTopology;
+  let _ := a.totalSpaceTopology; let _ := a.fiberTopology
   { totalSpaceMk_inducing' := a.inducing_totalSpaceMk,
     trivializationAtlas' :=
       { e | ∃ (e₀ : _) (he₀ : e₀ ∈ a.pretrivializationAtlas),
@@ -862,7 +862,7 @@ theorem continuous_proj : @Continuous _ _ a.totalSpaceTopology _ (π E) := by
 #align fiber_prebundle.continuous_proj FiberPrebundle.continuous_proj
 
 /-- For a fiber bundle `E` over `B` constructed using the `FiberPrebundle` mechanism,
-continuity of a function `total_space E → X` on an open set `s` can be checked by precomposing at
+continuity of a function `TotalSpace E → X` on an open set `s` can be checked by precomposing at
 each point with the pretrivialization used for the construction at that point. -/
 theorem continuousOn_of_comp_right {X : Type _} [TopologicalSpace X] {f : TotalSpace E → X}
     {s : Set B} (hs : IsOpen s) (hf : ∀ b ∈ s,