topology.gluing ⟷ Mathlib.Topology.Gluing

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

@@ -5,8 +5,8 @@ Authors: Andrew Yang
 -/
 import CategoryTheory.GlueData
 import CategoryTheory.ConcreteCategory.Elementwise
-import Topology.Category.Top.Limits.Pullbacks
-import Topology.Category.Top.Opens
+import Topology.Category.TopCat.Limits.Pullbacks
+import Topology.Category.TopCat.Opens
 
 #align_import topology.gluing from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
 

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

@@ -167,8 +167,8 @@ open CategoryTheory.Limits.WalkingParallelPair
 theorem eqvGen_of_π_eq {x y : ∐ D.U} (h : 𝖣.π x = 𝖣.π y) :
     EqvGen (Types.CoequalizerRel 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap) x y :=
   by
-  delta glue_data.π multicoequalizer.sigma_π at h 
-  simp_rw [comp_app] at h 
+  delta glue_data.π multicoequalizer.sigma_π at h
+  simp_rw [comp_app] at h
   replace h := (TopCat.mono_iff_injective (multicoequalizer.iso_coequalizer 𝖣.diagram).inv).mp _ h
   let diagram := parallel_pair 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap ⋙ forget _
   have : colimit.ι diagram one x = colimit.ι diagram one y :=
@@ -184,7 +184,7 @@ theorem eqvGen_of_π_eq {x y : ∐ D.U} (h : 𝖣.π x = 𝖣.π y) :
         this :
       _)
   simp only [eq_to_hom_refl, types_comp_apply, colimit.ι_map_assoc,
-    diagram_iso_parallel_pair_hom_app, colimit.iso_colimit_cocone_ι_hom, types_id_apply] at this 
+    diagram_iso_parallel_pair_hom_app, colimit.iso_colimit_cocone_ι_hom, types_id_apply] at this
   exact Quot.eq.1 this
   infer_instance
 #align Top.glue_data.eqv_gen_of_π_eq TopCat.GlueData.eqvGen_of_π_eq
@@ -347,7 +347,7 @@ structure MkCore where
 theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x :=
   by
   have := h.cocycle j i j x _
-  rw [h.t_id] at this 
+  rw [h.t_id] at this
   convert Subtype.eq this
   · ext; rfl
   all_goals rw [h.V_id]; trivial
@@ -451,8 +451,8 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
   intro x y e
   obtain ⟨i, ⟨x, hx⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective x
   obtain ⟨j, ⟨y, hy⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective y
-  rw [ι_from_open_subsets_glue_apply, ι_from_open_subsets_glue_apply] at e 
-  change x = y at e 
+  rw [ι_from_open_subsets_glue_apply, ι_from_open_subsets_glue_apply] at e
+  change x = y at e
   subst e
   rw [(of_open_subsets U).ι_eq_iff_rel]
   right
@@ -464,7 +464,7 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
 theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) :=
   by
   intro s hs
-  rw [(of_open_subsets U).isOpen_iff] at hs 
+  rw [(of_open_subsets U).isOpen_iff] at hs
   rw [isOpen_iff_forall_mem_open]
   rintro _ ⟨x, hx, rfl⟩
   obtain ⟨i, ⟨x, hx'⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective x

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.CategoryTheory.GlueData
-import Mathbin.CategoryTheory.ConcreteCategory.Elementwise
-import Mathbin.Topology.Category.Top.Limits.Pullbacks
-import Mathbin.Topology.Category.Top.Opens
+import CategoryTheory.GlueData
+import CategoryTheory.ConcreteCategory.Elementwise
+import Topology.Category.Top.Limits.Pullbacks
+import Topology.Category.Top.Opens
 
 #align_import topology.gluing from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -146,7 +146,7 @@ theorem rel_equiv : Equivalence D.Rel :=
     have eq₂ : (pullback.snd : _ ⟶ D.V _) z = y := pullback_iso_prod_subtype_inv_snd_apply _ _ _
     clear_value z
     right
-    use (pullback.fst : _ ⟶ D.V (i, k)) (D.t' _ _ _ z)
+    use(pullback.fst : _ ⟶ D.V (i, k)) (D.t' _ _ _ z)
     dsimp only at *
     substs e₁ e₃ e₄ eq₁ eq₂
     have h₁ : D.t' j i k ≫ pullback.fst ≫ D.f i k = pullback.fst ≫ D.t j i ≫ D.f i j := by

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module topology.gluing
-! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.GlueData
 import Mathbin.CategoryTheory.ConcreteCategory.Elementwise
 import Mathbin.Topology.Category.Top.Limits.Pullbacks
 import Mathbin.Topology.Category.Top.Opens
 
+#align_import topology.gluing from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
+
 /-!
 # Gluing Topological spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -66,6 +66,7 @@ open CategoryTheory.Limits
 
 namespace TopCat
 
+#print TopCat.GlueData /-
 /-- A family of gluing data consists of
 1. An index type `J`
 2. An object `U i` for each `i : J`.
@@ -93,6 +94,7 @@ structure GlueData extends GlueData TopCat where
   f_open : ∀ i j, OpenEmbedding (f i j)
   f_mono := fun i j => (TopCat.mono_iff_injective _).mpr (f_open i j).toEmbedding.inj
 #align Top.glue_data TopCat.GlueData
+-/
 
 namespace GlueData
 
@@ -100,10 +102,13 @@ variable (D : GlueData.{u})
 
 local notation "𝖣" => D.toGlueData
 
+#print TopCat.GlueData.π_surjective /-
 theorem π_surjective : Function.Surjective 𝖣.π :=
   (TopCat.epi_iff_surjective 𝖣.π).mp inferInstance
 #align Top.glue_data.π_surjective TopCat.GlueData.π_surjective
+-/
 
+#print TopCat.GlueData.isOpen_iff /-
 theorem isOpen_iff (U : Set 𝖣.glued) : IsOpen U ↔ ∀ i, IsOpen (𝖣.ι i ⁻¹' U) :=
   by
   delta CategoryTheory.GlueData.ι
@@ -114,18 +119,24 @@ theorem isOpen_iff (U : Set 𝖣.glued) : IsOpen U ↔ ∀ i, IsOpen (𝖣.ι i
   · intro h j; exact h ⟨j⟩
   · intro h j; cases j; exact h j
 #align Top.glue_data.is_open_iff TopCat.GlueData.isOpen_iff
+-/
 
+#print TopCat.GlueData.ι_jointly_surjective /-
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : _) (y : D.U i), 𝖣.ι i y = x :=
   𝖣.ι_jointly_surjective (forget TopCat) x
 #align Top.glue_data.ι_jointly_surjective TopCat.GlueData.ι_jointly_surjective
+-/
 
+#print TopCat.GlueData.Rel /-
 /-- An equivalence relation on `Σ i, D.U i` that holds iff `𝖣 .ι i x = 𝖣 .ι j y`.
 See `Top.glue_data.ι_eq_iff_rel`.
 -/
 def Rel (a b : Σ i, ((D.U i : TopCat) : Type _)) : Prop :=
   a = b ∨ ∃ x : D.V (a.1, b.1), D.f _ _ x = a.2 ∧ D.f _ _ (D.t _ _ x) = b.2
 #align Top.glue_data.rel TopCat.GlueData.Rel
+-/
 
+#print TopCat.GlueData.rel_equiv /-
 theorem rel_equiv : Equivalence D.Rel :=
   ⟨fun x => Or.inl (refl x), by
     rintro a b (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩)
@@ -151,9 +162,11 @@ theorem rel_equiv : Equivalence D.Rel :=
       exact pullback.condition.symm
     exact ⟨ContinuousMap.congr_fun h₁ z, ContinuousMap.congr_fun h₂ z⟩⟩
 #align Top.glue_data.rel_equiv TopCat.GlueData.rel_equiv
+-/
 
 open CategoryTheory.Limits.WalkingParallelPair
 
+#print TopCat.GlueData.eqvGen_of_π_eq /-
 theorem eqvGen_of_π_eq {x y : ∐ D.U} (h : 𝖣.π x = 𝖣.π y) :
     EqvGen (Types.CoequalizerRel 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap) x y :=
   by
@@ -178,7 +191,9 @@ theorem eqvGen_of_π_eq {x y : ∐ D.U} (h : 𝖣.π x = 𝖣.π y) :
   exact Quot.eq.1 this
   infer_instance
 #align Top.glue_data.eqv_gen_of_π_eq TopCat.GlueData.eqvGen_of_π_eq
+-/
 
+#print TopCat.GlueData.ι_eq_iff_rel /-
 theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
     𝖣.ι i x = 𝖣.ι j y ↔ D.Rel ⟨i, x⟩ ⟨j, y⟩ :=
   by
@@ -209,7 +224,9 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
     rfl; dsimp only at *; subst e₁; subst e₂; simp
 #align Top.glue_data.ι_eq_iff_rel TopCat.GlueData.ι_eq_iff_rel
+-/
 
+#print TopCat.GlueData.ι_injective /-
 theorem ι_injective (i : D.J) : Function.Injective (𝖣.ι i) :=
   by
   intro x y h
@@ -217,11 +234,15 @@ theorem ι_injective (i : D.J) : Function.Injective (𝖣.ι i) :=
   · rfl
   · dsimp only at *; cases e₁; cases e₂; simp
 #align Top.glue_data.ι_injective TopCat.GlueData.ι_injective
+-/
 
+#print TopCat.GlueData.ι_mono /-
 instance ι_mono (i : D.J) : Mono (𝖣.ι i) :=
   (TopCat.mono_iff_injective _).mpr (D.ι_injective _)
 #align Top.glue_data.ι_mono TopCat.GlueData.ι_mono
+-/
 
+#print TopCat.GlueData.image_inter /-
 theorem image_inter (i j : D.J) :
     Set.range (𝖣.ι i) ∩ Set.range (𝖣.ι j) = Set.range (D.f i j ≫ 𝖣.ι _) :=
   by
@@ -234,13 +255,17 @@ theorem image_inter (i j : D.J) :
   · rintro ⟨x, hx⟩
     exact ⟨⟨D.f i j x, hx⟩, ⟨D.f j i (D.t _ _ x), by simp [← hx]⟩⟩
 #align Top.glue_data.image_inter TopCat.GlueData.image_inter
+-/
 
+#print TopCat.GlueData.preimage_range /-
 theorem preimage_range (i j : D.J) : 𝖣.ι j ⁻¹' Set.range (𝖣.ι i) = Set.range (D.f j i) := by
   rw [← Set.preimage_image_eq (Set.range (D.f j i)) (D.ι_injective j), ← Set.image_univ, ←
     Set.image_univ, ← Set.image_comp, ← coe_comp, Set.image_univ, Set.image_univ, ← image_inter,
     Set.preimage_range_inter]
 #align Top.glue_data.preimage_range TopCat.GlueData.preimage_range
+-/
 
+#print TopCat.GlueData.preimage_image_eq_image /-
 theorem preimage_image_eq_image (i j : D.J) (U : Set (𝖣.U i)) :
     𝖣.ι j ⁻¹' (𝖣.ι i '' U) = D.f _ _ '' ((D.t j i ≫ D.f _ _) ⁻¹' U) :=
   by
@@ -256,7 +281,9 @@ theorem preimage_image_eq_image (i j : D.J) (U : Set (𝖣.U i)) :
   rw [← D.preimage_range i j]
   exact Set.preimage_mono (Set.image_subset_range _ _)
 #align Top.glue_data.preimage_image_eq_image TopCat.GlueData.preimage_image_eq_image
+-/
 
+#print TopCat.GlueData.preimage_image_eq_image' /-
 theorem preimage_image_eq_image' (i j : D.J) (U : Set (𝖣.U i)) :
     𝖣.ι j ⁻¹' (𝖣.ι i '' U) = (D.t i j ≫ D.f _ _) '' (D.f _ _ ⁻¹' U) :=
   by
@@ -269,7 +296,9 @@ theorem preimage_image_eq_image' (i j : D.J) (U : Set (𝖣.U i)) :
   rw [← is_iso_iff_bijective]
   apply (forget TopCat).map_isIso
 #align Top.glue_data.preimage_image_eq_image' TopCat.GlueData.preimage_image_eq_image'
+-/
 
+#print TopCat.GlueData.open_image_open /-
 theorem open_image_open (i : D.J) (U : Opens (𝖣.U i)) : IsOpen (𝖣.ι i '' U) :=
   by
   rw [is_open_iff]
@@ -279,12 +308,16 @@ theorem open_image_open (i : D.J) (U : Opens (𝖣.U i)) : IsOpen (𝖣.ι i ''
   apply (D.t j i ≫ D.f i j).continuous_toFun.isOpen_preimage
   exact U.is_open
 #align Top.glue_data.open_image_open TopCat.GlueData.open_image_open
+-/
 
+#print TopCat.GlueData.ι_openEmbedding /-
 theorem ι_openEmbedding (i : D.J) : OpenEmbedding (𝖣.ι i) :=
   openEmbedding_of_continuous_injective_open (𝖣.ι i).continuous_toFun (D.ι_injective i) fun U h =>
     D.open_image_open i ⟨U, h⟩
 #align Top.glue_data.ι_open_embedding TopCat.GlueData.ι_openEmbedding
+-/
 
+#print TopCat.GlueData.MkCore /-
 /-- A family of gluing data consists of
 1. An index type `J`
 2. A bundled topological space `U i` for each `i : J`.
@@ -311,7 +344,9 @@ structure MkCore where
     ∀ (i j k) (x : V i j) (h : ↑x ∈ V i k),
       @coe (V k j) (U k) _ (t j k ⟨↑(t i j x), t_inter k x h⟩) = @coe (V k i) (U k) _ (t i k ⟨x, h⟩)
 #align Top.glue_data.mk_core TopCat.GlueData.MkCore
+-/
 
+#print TopCat.GlueData.MkCore.t_inv /-
 theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x :=
   by
   have := h.cocycle j i j x _
@@ -320,10 +355,12 @@ theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i)
   · ext; rfl
   all_goals rw [h.V_id]; trivial
 #align Top.glue_data.mk_core.t_inv TopCat.GlueData.MkCore.t_inv
+-/
 
 instance (h : MkCore.{u}) (i j : h.J) : IsIso (h.t i j) := by use h.t j i; constructor <;> ext1;
   exacts [h.t_inv _ _ _, h.t_inv _ _ _]
 
+#print TopCat.GlueData.MkCore.t' /-
 /-- (Implementation) the restricted transition map to be fed into `glue_data`. -/
 def MkCore.t' (h : MkCore.{u}) (i j k : h.J) :
     pullback (h.V i j).inclusion (h.V i k).inclusion ⟶
@@ -336,7 +373,9 @@ def MkCore.t' (h : MkCore.{u}) (i j k : h.J) :
     exact h.t_inter _ ⟨x, hx⟩ hx'
   continuity
 #align Top.glue_data.mk_core.t' TopCat.GlueData.MkCore.t'
+-/
 
+#print TopCat.GlueData.mk' /-
 /-- This is a constructor of `Top.glue_data` whose arguments are in terms of elements and
 intersections rather than subobjects and pullbacks. Please refer to `Top.glue_data.mk_core` for
 details. -/
@@ -371,9 +410,11 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData
     ext
     exact h.cocycle i j k ⟨x, hx⟩ hx'
 #align Top.glue_data.mk' TopCat.GlueData.mk'
+-/
 
 variable {α : Type u} [TopologicalSpace α] {J : Type u} (U : J → Opens α)
 
+#print TopCat.GlueData.ofOpenSubsets /-
 /-- We may construct a glue data from a family of open sets. -/
 @[simps to_glue_data_J to_glue_data_U to_glue_data_V to_glue_data_t to_glue_data_f]
 def ofOpenSubsets : TopCat.GlueData.{u} :=
@@ -387,7 +428,9 @@ def ofOpenSubsets : TopCat.GlueData.{u} :=
       t_inter := fun i j k x hx => hx
       cocycle := fun i j k x h => rfl }
 #align Top.glue_data.of_open_subsets TopCat.GlueData.ofOpenSubsets
+-/
 
+#print TopCat.GlueData.fromOpenSubsetsGlue /-
 /-- The canonical map from the glue of a family of open subsets `α` into `α`.
 This map is an open embedding (`from_open_subsets_glue_open_embedding`),
 and its range is `⋃ i, (U i : set α)` (`range_from_open_subsets_glue`).
@@ -395,13 +438,17 @@ and its range is `⋃ i, (U i : set α)` (`range_from_open_subsets_glue`).
 def fromOpenSubsetsGlue : (ofOpenSubsets U).toGlueData.glued ⟶ TopCat.of α :=
   Multicoequalizer.desc _ _ (fun x => Opens.inclusion _) (by rintro ⟨i, j⟩; ext x; rfl)
 #align Top.glue_data.from_open_subsets_glue TopCat.GlueData.fromOpenSubsetsGlue
+-/
 
+#print TopCat.GlueData.ι_fromOpenSubsetsGlue /-
 @[simp, elementwise]
 theorem ι_fromOpenSubsetsGlue (i : J) :
     (ofOpenSubsets U).toGlueData.ι i ≫ fromOpenSubsetsGlue U = Opens.inclusion _ :=
   Multicoequalizer.π_desc _ _ _ _ _
 #align Top.glue_data.ι_from_open_subsets_glue TopCat.GlueData.ι_fromOpenSubsetsGlue
+-/
 
+#print TopCat.GlueData.fromOpenSubsetsGlue_injective /-
 theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue U) :=
   by
   intro x y e
@@ -414,7 +461,9 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
   right
   exact ⟨⟨⟨x, hx⟩, hy⟩, rfl, rfl⟩
 #align Top.glue_data.from_open_subsets_glue_injective TopCat.GlueData.fromOpenSubsetsGlue_injective
+-/
 
+#print TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap /-
 theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) :=
   by
   intro s hs
@@ -435,12 +484,16 @@ theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) :=
     rw [ι_from_open_subsets_glue_apply]
     exact Set.mem_range_self _
 #align Top.glue_data.from_open_subsets_glue_is_open_map TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap
+-/
 
+#print TopCat.GlueData.fromOpenSubsetsGlue_openEmbedding /-
 theorem fromOpenSubsetsGlue_openEmbedding : OpenEmbedding (fromOpenSubsetsGlue U) :=
   openEmbedding_of_continuous_injective_open (ContinuousMap.continuous_toFun _)
     (fromOpenSubsetsGlue_injective U) (fromOpenSubsetsGlue_isOpenMap U)
 #align Top.glue_data.from_open_subsets_glue_open_embedding TopCat.GlueData.fromOpenSubsetsGlue_openEmbedding
+-/
 
+#print TopCat.GlueData.range_fromOpenSubsetsGlue /-
 theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (U i : Set α) :=
   by
   ext
@@ -452,7 +505,9 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
   · rintro ⟨_, ⟨i, rfl⟩, hx⟩
     refine' ⟨(of_open_subsets U).toGlueData.ι i ⟨x, hx⟩, ι_from_open_subsets_glue_apply _ _ _⟩
 #align Top.glue_data.range_from_open_subsets_glue TopCat.GlueData.range_fromOpenSubsetsGlue
+-/
 
+#print TopCat.GlueData.openCoverGlueHomeo /-
 /-- The gluing of an open cover is homeomomorphic to the original space. -/
 def openCoverGlueHomeo (h : (⋃ i, (U i : Set α)) = Set.univ) :
     (ofOpenSubsets U).toGlueData.glued ≃ₜ α :=
@@ -462,6 +517,7 @@ def openCoverGlueHomeo (h : (⋃ i, (U i : Set α)) = Set.univ) :
         Set.range_iff_surjective.mp ((range_fromOpenSubsetsGlue U).symm ▸ h)⟩)
     (fromOpenSubsetsGlue U).2 (fromOpenSubsetsGlue_isOpenMap U)
 #align Top.glue_data.open_cover_glue_homeo TopCat.GlueData.openCoverGlueHomeo
+-/
 
 end GlueData
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf9bbbcf0c1c1ead18280b0d010e417b10abb1b6

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.gluing
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
+! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Category.Top.Opens
 /-!
 # Gluing Topological spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a family of gluing data (see `category_theory/glue_data`), we can then glue them together.
 
 The construction should be "sealed" and considered as a black box, while only using the API

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

@@ -95,7 +95,6 @@ namespace GlueData
 
 variable (D : GlueData.{u})
 
--- mathport name: «expr𝖣»
 local notation "𝖣" => D.toGlueData
 
 theorem π_surjective : Function.Surjective 𝖣.π :=
@@ -372,8 +371,6 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData
 
 variable {α : Type u} [TopologicalSpace α] {J : Type u} (U : J → Opens α)
 
-include U
-
 /-- We may construct a glue data from a family of open sets. -/
 @[simps to_glue_data_J to_glue_data_U to_glue_data_V to_glue_data_t to_glue_data_f]
 def ofOpenSubsets : TopCat.GlueData.{u} :=

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

@@ -113,21 +113,21 @@ theorem isOpen_iff (U : Set 𝖣.glued) : IsOpen U ↔ ∀ i, IsOpen (𝖣.ι i
   · intro h j; cases j; exact h j
 #align Top.glue_data.is_open_iff TopCat.GlueData.isOpen_iff
 
-theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : _)(y : D.U i), 𝖣.ι i y = x :=
+theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : _) (y : D.U i), 𝖣.ι i y = x :=
   𝖣.ι_jointly_surjective (forget TopCat) x
 #align Top.glue_data.ι_jointly_surjective TopCat.GlueData.ι_jointly_surjective
 
 /-- An equivalence relation on `Σ i, D.U i` that holds iff `𝖣 .ι i x = 𝖣 .ι j y`.
 See `Top.glue_data.ι_eq_iff_rel`.
 -/
-def Rel (a b : Σi, ((D.U i : TopCat) : Type _)) : Prop :=
+def Rel (a b : Σ i, ((D.U i : TopCat) : Type _)) : Prop :=
   a = b ∨ ∃ x : D.V (a.1, b.1), D.f _ _ x = a.2 ∧ D.f _ _ (D.t _ _ x) = b.2
 #align Top.glue_data.rel TopCat.GlueData.Rel
 
 theorem rel_equiv : Equivalence D.Rel :=
   ⟨fun x => Or.inl (refl x), by
     rintro a b (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩)
-    exacts[Or.inl rfl, Or.inr ⟨D.t _ _ x, by simp [e₁, e₂]⟩],
+    exacts [Or.inl rfl, Or.inr ⟨D.t _ _ x, by simp [e₁, e₂]⟩],
     by
     rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩); exact id
     rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩); exact Or.inr ⟨x, e₁, e₂⟩
@@ -155,8 +155,8 @@ open CategoryTheory.Limits.WalkingParallelPair
 theorem eqvGen_of_π_eq {x y : ∐ D.U} (h : 𝖣.π x = 𝖣.π y) :
     EqvGen (Types.CoequalizerRel 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap) x y :=
   by
-  delta glue_data.π multicoequalizer.sigma_π at h
-  simp_rw [comp_app] at h
+  delta glue_data.π multicoequalizer.sigma_π at h 
+  simp_rw [comp_app] at h 
   replace h := (TopCat.mono_iff_injective (multicoequalizer.iso_coequalizer 𝖣.diagram).inv).mp _ h
   let diagram := parallel_pair 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap ⋙ forget _
   have : colimit.ι diagram one x = colimit.ι diagram one y :=
@@ -172,7 +172,7 @@ theorem eqvGen_of_π_eq {x y : ∐ D.U} (h : 𝖣.π x = 𝖣.π y) :
         this :
       _)
   simp only [eq_to_hom_refl, types_comp_apply, colimit.ι_map_assoc,
-    diagram_iso_parallel_pair_hom_app, colimit.iso_colimit_cocone_ι_hom, types_id_apply] at this
+    diagram_iso_parallel_pair_hom_app, colimit.iso_colimit_cocone_ι_hom, types_id_apply] at this 
   exact Quot.eq.1 this
   infer_instance
 #align Top.glue_data.eqv_gen_of_π_eq TopCat.GlueData.eqvGen_of_π_eq
@@ -313,14 +313,14 @@ structure MkCore where
 theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x :=
   by
   have := h.cocycle j i j x _
-  rw [h.t_id] at this
+  rw [h.t_id] at this 
   convert Subtype.eq this
   · ext; rfl
   all_goals rw [h.V_id]; trivial
 #align Top.glue_data.mk_core.t_inv TopCat.GlueData.MkCore.t_inv
 
 instance (h : MkCore.{u}) (i j : h.J) : IsIso (h.t i j) := by use h.t j i; constructor <;> ext1;
-  exacts[h.t_inv _ _ _, h.t_inv _ _ _]
+  exacts [h.t_inv _ _ _, h.t_inv _ _ _]
 
 /-- (Implementation) the restricted transition map to be fed into `glue_data`. -/
 def MkCore.t' (h : MkCore.{u}) (i j k : h.J) :
@@ -407,8 +407,8 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
   intro x y e
   obtain ⟨i, ⟨x, hx⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective x
   obtain ⟨j, ⟨y, hy⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective y
-  rw [ι_from_open_subsets_glue_apply, ι_from_open_subsets_glue_apply] at e
-  change x = y at e
+  rw [ι_from_open_subsets_glue_apply, ι_from_open_subsets_glue_apply] at e 
+  change x = y at e 
   subst e
   rw [(of_open_subsets U).ι_eq_iff_rel]
   right
@@ -418,7 +418,7 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
 theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) :=
   by
   intro s hs
-  rw [(of_open_subsets U).isOpen_iff] at hs
+  rw [(of_open_subsets U).isOpen_iff] at hs 
   rw [isOpen_iff_forall_mem_open]
   rintro _ ⟨x, hx, rfl⟩
   obtain ⟨i, ⟨x, hx'⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective x

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

@@ -109,11 +109,8 @@ theorem isOpen_iff (U : Set 𝖣.glued) : IsOpen U ↔ ∀ i, IsOpen (𝖣.ι i
   rw [← (homeo_of_iso (multicoequalizer.iso_coequalizer 𝖣.diagram).symm).isOpen_preimage]
   rw [coequalizer_is_open_iff, colimit_isOpen_iff.{u}]
   constructor
-  · intro h j
-    exact h ⟨j⟩
-  · intro h j
-    cases j
-    exact h j
+  · intro h j; exact h ⟨j⟩
+  · intro h j; cases j; exact h j
 #align Top.glue_data.is_open_iff TopCat.GlueData.isOpen_iff
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : _)(y : D.U i), 𝖣.ι i y = x :=
@@ -132,10 +129,8 @@ theorem rel_equiv : Equivalence D.Rel :=
     rintro a b (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩)
     exacts[Or.inl rfl, Or.inr ⟨D.t _ _ x, by simp [e₁, e₂]⟩],
     by
-    rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩)
-    exact id
-    rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩)
-    exact Or.inr ⟨x, e₁, e₂⟩
+    rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩); exact id
+    rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩); exact Or.inr ⟨x, e₁, e₂⟩
     let z := (pullback_iso_prod_subtype (D.f j i) (D.f j k)).inv ⟨⟨_, _⟩, e₂.trans e₃.symm⟩
     have eq₁ : (D.t j i) ((pullback.fst : _ ⟶ D.V _) z) = x := by simp
     have eq₂ : (pullback.snd : _ ⟶ D.V _) z = y := pullback_iso_prod_subtype_inv_snd_apply _ _ _
@@ -144,11 +139,8 @@ theorem rel_equiv : Equivalence D.Rel :=
     use (pullback.fst : _ ⟶ D.V (i, k)) (D.t' _ _ _ z)
     dsimp only at *
     substs e₁ e₃ e₄ eq₁ eq₂
-    have h₁ : D.t' j i k ≫ pullback.fst ≫ D.f i k = pullback.fst ≫ D.t j i ≫ D.f i j :=
-      by
-      rw [← 𝖣.t_fac_assoc]
-      congr 1
-      exact pullback.condition
+    have h₁ : D.t' j i k ≫ pullback.fst ≫ D.f i k = pullback.fst ≫ D.t j i ≫ D.f i j := by
+      rw [← 𝖣.t_fac_assoc]; congr 1; exact pullback.condition
     have h₂ : D.t' j i k ≫ pullback.fst ≫ D.t i k ≫ D.f k i = pullback.snd ≫ D.t j k ≫ D.f k j :=
       by
       rw [← 𝖣.t_fac_assoc]
@@ -211,17 +203,9 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
       CategoryTheory.Limits.colimit.ι_desc_apply, cofan.mk_ι_app, sigma_iso_sigma_hom_ι_apply,
       ContinuousMap.toFun_eq_coe]
     erw [sigma_iso_sigma_hom_ι_apply, sigma_iso_sigma_hom_ι_apply]
-    exact
-      Or.inr
-        ⟨y, by
-          dsimp [glue_data.diagram]
-          simp⟩
+    exact Or.inr ⟨y, by dsimp [glue_data.diagram]; simp⟩
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
-    rfl
-    dsimp only at *
-    subst e₁
-    subst e₂
-    simp
+    rfl; dsimp only at *; subst e₁; subst e₂; simp
 #align Top.glue_data.ι_eq_iff_rel TopCat.GlueData.ι_eq_iff_rel
 
 theorem ι_injective (i : D.J) : Function.Injective (𝖣.ι i) :=
@@ -229,10 +213,7 @@ theorem ι_injective (i : D.J) : Function.Injective (𝖣.ι i) :=
   intro x y h
   rcases(D.ι_eq_iff_rel _ _ _ _).mp h with (⟨⟨⟩⟩ | ⟨_, e₁, e₂⟩)
   · rfl
-  · dsimp only at *
-    cases e₁
-    cases e₂
-    simp
+  · dsimp only at *; cases e₁; cases e₂; simp
 #align Top.glue_data.ι_injective TopCat.GlueData.ι_injective
 
 instance ι_mono (i : D.J) : Mono (𝖣.ι i) :=
@@ -247,9 +228,7 @@ theorem image_inter (i j : D.J) :
   · rintro ⟨⟨x₁, eq₁⟩, ⟨x₂, eq₂⟩⟩
     obtain ⟨⟨⟩⟩ | ⟨y, e₁, e₂⟩ := (D.ι_eq_iff_rel _ _ _ _).mp (eq₁.trans eq₂.symm)
     · exact ⟨inv (D.f i i) x₁, by simp [eq₁]⟩
-    · dsimp only at *
-      substs e₁ eq₁
-      exact ⟨y, by simp⟩
+    · dsimp only at *; substs e₁ eq₁; exact ⟨y, by simp⟩
   · rintro ⟨x, hx⟩
     exact ⟨⟨D.f i j x, hx⟩, ⟨D.f j i (D.t _ _ x), by simp [← hx]⟩⟩
 #align Top.glue_data.image_inter TopCat.GlueData.image_inter
@@ -336,15 +315,11 @@ theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i)
   have := h.cocycle j i j x _
   rw [h.t_id] at this
   convert Subtype.eq this
-  · ext
-    rfl
+  · ext; rfl
   all_goals rw [h.V_id]; trivial
 #align Top.glue_data.mk_core.t_inv TopCat.GlueData.MkCore.t_inv
 
-instance (h : MkCore.{u}) (i j : h.J) : IsIso (h.t i j) :=
-  by
-  use h.t j i
-  constructor <;> ext1
+instance (h : MkCore.{u}) (i j : h.J) : IsIso (h.t i j) := by use h.t j i; constructor <;> ext1;
   exacts[h.t_inv _ _ _, h.t_inv _ _ _]
 
 /-- (Implementation) the restricted transition map to be fed into `glue_data`. -/
@@ -372,10 +347,7 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData
   f_id i := (h.v_id i).symm ▸ IsIso.of_iso (Opens.inclusionTopIso (h.U i))
   f_open := fun i j : h.J => (h.V i j).OpenEmbedding
   t := h.t
-  t_id i := by
-    ext
-    rw [h.t_id]
-    rfl
+  t_id i := by ext; rw [h.t_id]; rfl
   t' := h.t'
   t_fac i j k := by
     delta mk_core.t'
@@ -410,13 +382,8 @@ def ofOpenSubsets : TopCat.GlueData.{u} :=
       U := fun i => (Opens.toTopCat <| TopCat.of α).obj (U i)
       V := fun i j => (Opens.map <| Opens.inclusion _).obj (U j)
       t := fun i j => ⟨fun x => ⟨⟨x.1.1, x.2⟩, x.1.2⟩, by continuity⟩
-      v_id := fun i => by
-        ext
-        cases U i
-        simp
-      t_id := fun i => by
-        ext
-        rfl
+      v_id := fun i => by ext; cases U i; simp
+      t_id := fun i => by ext; rfl
       t_inter := fun i j k x hx => hx
       cocycle := fun i j k x h => rfl }
 #align Top.glue_data.of_open_subsets TopCat.GlueData.ofOpenSubsets
@@ -426,11 +393,7 @@ This map is an open embedding (`from_open_subsets_glue_open_embedding`),
 and its range is `⋃ i, (U i : set α)` (`range_from_open_subsets_glue`).
 -/
 def fromOpenSubsetsGlue : (ofOpenSubsets U).toGlueData.glued ⟶ TopCat.of α :=
-  Multicoequalizer.desc _ _ (fun x => Opens.inclusion _)
-    (by
-      rintro ⟨i, j⟩
-      ext x
-      rfl)
+  Multicoequalizer.desc _ _ (fun x => Opens.inclusion _) (by rintro ⟨i, j⟩; ext x; rfl)
 #align Top.glue_data.from_open_subsets_glue TopCat.GlueData.fromOpenSubsetsGlue
 
 @[simp, elementwise]

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

@@ -485,7 +485,7 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
   · rintro ⟨x, rfl⟩
     obtain ⟨i, ⟨x, hx'⟩, rfl⟩ := (of_open_subsets U).ι_jointly_surjective x
     rw [ι_from_open_subsets_glue_apply]
-    exact Set.subset_unionᵢ _ i hx'
+    exact Set.subset_iUnion _ i hx'
   · rintro ⟨_, ⟨i, rfl⟩, hx⟩
     refine' ⟨(of_open_subsets U).toGlueData.ι i ⟨x, hx⟩, ι_from_open_subsets_glue_apply _ _ _⟩
 #align Top.glue_data.range_from_open_subsets_glue TopCat.GlueData.range_fromOpenSubsetsGlue

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -322,7 +322,7 @@ structure MkCore where
   {J : Type u}
   U : J → TopCat.{u}
   V : ∀ i, J → Opens (U i)
-  t : ∀ i j, (Opens.toTop _).obj (V i j) ⟶ (Opens.toTop _).obj (V j i)
+  t : ∀ i j, (Opens.toTopCat _).obj (V i j) ⟶ (Opens.toTopCat _).obj (V j i)
   v_id : ∀ i, V i i = ⊤
   t_id : ∀ i, ⇑(t i i) = id
   t_inter : ∀ ⦃i j⦄ (k) (x : V i j), ↑x ∈ V i k → @coe (V j i) (U j) _ (t i j x) ∈ V j k
@@ -367,7 +367,7 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData
     where
   J := h.J
   U := h.U
-  V i := (Opens.toTop _).obj (h.V i.1 i.2)
+  V i := (Opens.toTopCat _).obj (h.V i.1 i.2)
   f i j := (h.V i j).inclusion
   f_id i := (h.v_id i).symm ▸ IsIso.of_iso (Opens.inclusionTopIso (h.U i))
   f_open := fun i j : h.J => (h.V i j).OpenEmbedding
@@ -407,7 +407,7 @@ include U
 def ofOpenSubsets : TopCat.GlueData.{u} :=
   mk'.{u}
     { J
-      U := fun i => (Opens.toTop <| TopCat.of α).obj (U i)
+      U := fun i => (Opens.toTopCat <| TopCat.of α).obj (U i)
       V := fun i j => (Opens.map <| Opens.inclusion _).obj (U j)
       t := fun i j => ⟨fun x => ⟨⟨x.1.1, x.2⟩, x.1.2⟩, by continuity⟩
       v_id := fun i => by

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.gluing
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
+! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.GlueData
 import Mathbin.CategoryTheory.ConcreteCategory.Elementwise
-import Mathbin.Topology.Category.Top.Limits
+import Mathbin.Topology.Category.Top.Limits.Pullbacks
 import Mathbin.Topology.Category.Top.Opens
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -426,7 +426,7 @@ This map is an open embedding (`from_open_subsets_glue_open_embedding`),
 and its range is `⋃ i, (U i : set α)` (`range_from_open_subsets_glue`).
 -/
 def fromOpenSubsetsGlue : (ofOpenSubsets U).toGlueData.glued ⟶ TopCat.of α :=
-  multicoequalizer.desc _ _ (fun x => Opens.inclusion _)
+  Multicoequalizer.desc _ _ (fun x => Opens.inclusion _)
     (by
       rintro ⟨i, j⟩
       ext x
@@ -436,7 +436,7 @@ def fromOpenSubsetsGlue : (ofOpenSubsets U).toGlueData.glued ⟶ TopCat.of α :=
 @[simp, elementwise]
 theorem ι_fromOpenSubsetsGlue (i : J) :
     (ofOpenSubsets U).toGlueData.ι i ≫ fromOpenSubsetsGlue U = Opens.inclusion _ :=
-  multicoequalizer.π_desc _ _ _ _ _
+  Multicoequalizer.π_desc _ _ _ _ _
 #align Top.glue_data.ι_from_open_subsets_glue TopCat.GlueData.ι_fromOpenSubsetsGlue
 
 theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue U) :=

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -132,8 +132,10 @@ theorem rel_equiv : Equivalence D.Rel :=
   ⟨fun x => Or.inl (refl x), by
     rintro a b (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩)
     exacts [Or.inl rfl, Or.inr ⟨D.t _ _ x, by simp [e₁, e₂]⟩], by
-    rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩); exact id
-    rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩); exact Or.inr ⟨x, e₁, e₂⟩
+    rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩)
+    · exact id
+    rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩)
+    · exact Or.inr ⟨x, e₁, e₂⟩
     let z := (pullbackIsoProdSubtype (D.f j i) (D.f j k)).inv ⟨⟨_, _⟩, e₂.trans e₃.symm⟩
     have eq₁ : (D.t j i) ((pullback.fst : _ /-(D.f j k)-/ ⟶ D.V (j, i)) z) = x := by simp [z]
     have eq₂ : (pullback.snd : _ ⟶ D.V _) z = y := pullbackIsoProdSubtype_inv_snd_apply _ _ _
@@ -219,7 +221,7 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
     erw [sigmaIsoSigma_hom_ι_apply, sigmaIsoSigma_hom_ι_apply]
     exact Or.inr ⟨y, ⟨rfl, rfl⟩⟩
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
-    rfl
+    · rfl
     dsimp only at *
     -- Porting note: there were `subst e₁` and `subst e₂`, instead of the `rw`
     rw [← e₁, ← e₂] at *
@@ -297,8 +299,8 @@ theorem preimage_image_eq_image' (i j : D.J) (U : Set (𝖣.U i)) :
   -- Porting note: `congr 1` was here, instead of `congr_arg`, however, it did nothing.
   refine congr_arg ?_ ?_
   rw [← Set.eq_preimage_iff_image_eq, Set.preimage_preimage]
-  change _ = (D.t i j ≫ D.t j i ≫ _) ⁻¹' _
-  rw [𝖣.t_inv_assoc]
+  · change _ = (D.t i j ≫ D.t j i ≫ _) ⁻¹' _
+    rw [𝖣.t_inv_assoc]
   rw [← isIso_iff_bijective]
   apply (forget TopCat).map_isIso
 set_option linter.uppercaseLean3 false in
@@ -353,10 +355,10 @@ set_option linter.uppercaseLean3 false in
 
 theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x := by
   have := h.cocycle j i j x ?_
-  rw [h.t_id] at this
-  convert Subtype.eq this
-  rw [h.V_id]
-  trivial
+  · rw [h.t_id] at this
+    · convert Subtype.eq this
+    rw [h.V_id]
+    trivial
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.mk_core.t_inv TopCat.GlueData.MkCore.t_inv
 

This subsumes some of the notes in #10752 and #10971. I'm on the fence as to whether replacing the dsimp only by beta_reduce is useful; this is easy to revert if needed.

@@ -389,8 +389,8 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
   V i := (Opens.toTopCat _).obj (h.V i.1 i.2)
   f i j := (h.V i j).inclusion
   f_id i := by
-    -- Porting note (#10752): added `dsimp only`
-    dsimp only
+    -- Porting note (#12129): additional beta reduction needed
+    beta_reduce
     exact (h.V_id i).symm ▸ IsIso.of_iso (Opens.inclusionTopIso (h.U i))
   f_open := fun i j : h.J => (h.V i j).openEmbedding
   t := h.t

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.

@@ -82,7 +82,7 @@ that the `U i`'s are open subspaces of the glued space.
 Most of the times it would be easier to use the constructor `TopCat.GlueData.mk'` where the
 conditions are stated in a less categorical way.
 -/
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 structure GlueData extends GlueData TopCat where
   f_open : ∀ i j, OpenEmbedding (f i j)
   f_mono := fun i j => (TopCat.mono_iff_injective _).mpr (f_open i j).toEmbedding.inj
@@ -335,7 +335,7 @@ such that
 
 We can then glue the topological spaces `U i` together by identifying `V i j` with `V j i`.
 -/
--- Porting note: removed `@[nolint has_nonempty_instance]`
+-- Porting note(#5171): removed `@[nolint has_nonempty_instance]`
 structure MkCore where
   {J : Type u}
   U : J → TopCat.{u}

@@ -210,18 +210,10 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
     rw [← (InvImage.equivalence _ _ D.rel_equiv).eqvGen_iff]
     refine' EqvGen.mono _ (D.eqvGen_of_π_eq h : _)
     rintro _ _ ⟨x⟩
-    rw [← show (sigmaIsoSigma.{u, u} _).inv _ = x from
-        ConcreteCategory.congr_hom (sigmaIsoSigma.{u, u} _).hom_inv_id x]
-  -- Adaption note: v4.7.0-rc1
-  -- The behaviour of `generalize` was changed in https://github.com/leanprover/lean4/pull/3575
-  -- to use transparancy `instances` (rather than `default`)
-  -- `generalize'` is a temporary backwards compatibility shim.
-  -- Hopefully we will be able to refactor this proof to use `generalize` again, and then drop
-  -- `generalize'`.
-    generalize' h : (sigmaIsoSigma.{u, u} D.V).hom x = x'
-    obtain ⟨⟨i, j⟩, y⟩ := x'
+    obtain ⟨⟨⟨i, j⟩, y⟩, rfl⟩ :=
+      (ConcreteCategory.bijective_of_isIso (sigmaIsoSigma.{u, u} _).inv).2 x
     unfold InvImage MultispanIndex.fstSigmaMap MultispanIndex.sndSigmaMap
-    simp only [Opens.inclusion_apply, TopCat.comp_app, sigmaIsoSigma_inv_apply,
+    simp only [forget_map_eq_coe, Opens.inclusion_apply, TopCat.comp_app, sigmaIsoSigma_inv_apply,
       Cofan.mk_ι_app]
     rw [← comp_apply, colimit.ι_desc, ← comp_apply, colimit.ι_desc]
     erw [sigmaIsoSigma_hom_ι_apply, sigmaIsoSigma_hom_ι_apply]

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -6,6 +6,7 @@ Authors: Andrew Yang
 import Mathlib.CategoryTheory.GlueData
 import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
 import Mathlib.Topology.Category.TopCat.Opens
+import Mathlib.Tactic.Generalize
 
 #align_import topology.gluing from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 
@@ -211,7 +212,13 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
     rintro _ _ ⟨x⟩
     rw [← show (sigmaIsoSigma.{u, u} _).inv _ = x from
         ConcreteCategory.congr_hom (sigmaIsoSigma.{u, u} _).hom_inv_id x]
-    generalize (sigmaIsoSigma.{u, u} D.V).hom x = x'
+  -- Adaption note: v4.7.0-rc1
+  -- The behaviour of `generalize` was changed in https://github.com/leanprover/lean4/pull/3575
+  -- to use transparancy `instances` (rather than `default`)
+  -- `generalize'` is a temporary backwards compatibility shim.
+  -- Hopefully we will be able to refactor this proof to use `generalize` again, and then drop
+  -- `generalize'`.
+    generalize' h : (sigmaIsoSigma.{u, u} D.V).hom x = x'
     obtain ⟨⟨i, j⟩, y⟩ := x'
     unfold InvImage MultispanIndex.fstSigmaMap MultispanIndex.sndSigmaMap
     simp only [Opens.inclusion_apply, TopCat.comp_app, sigmaIsoSigma_inv_apply,
@@ -375,6 +382,7 @@ def MkCore.t' (h : MkCore.{u}) (i j k : h.J) :
     exact h.t_inter _ ⟨x, hx⟩ hx'
   -- Porting note: was `continuity`, see https://github.com/leanprover-community/mathlib4/issues/5030
   have : Continuous (h.t i j) := map_continuous (self := ContinuousMap.toContinuousMapClass) _
+  set_option tactic.skipAssignedInstances false in
   exact ((Continuous.subtype_mk (by continuity) _).prod_mk (by continuity)).subtype_mk _
 
 set_option linter.uppercaseLean3 false in

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".

@@ -106,7 +106,7 @@ theorem isOpen_iff (U : Set 𝖣.glued) : IsOpen U ↔ ∀ i, IsOpen (𝖣.ι i
   rw [coequalizer_isOpen_iff]
   dsimp only [GlueData.diagram_l, GlueData.diagram_left, GlueData.diagram_r, GlueData.diagram_right,
     parallelPair_obj_one]
-  rw [colimit_isOpen_iff.{_,u}]  -- porting note: changed `.{u}` to `.{_,u}`.  fun fact: the proof
+  rw [colimit_isOpen_iff.{_,u}]  -- Porting note: changed `.{u}` to `.{_,u}`.  fun fact: the proof
                                  -- breaks down if this `rw` is merged with the `rw` above.
   constructor
   · intro h j; exact h ⟨j⟩
@@ -222,7 +222,7 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
     rfl
     dsimp only at *
-    -- porting note: there were `subst e₁` and `subst e₂`, instead of the `rw`
+    -- Porting note: there were `subst e₁` and `subst e₂`, instead of the `rw`
     rw [← e₁, ← e₂] at *
     simp
 set_option linter.uppercaseLean3 false in
@@ -233,7 +233,7 @@ theorem ι_injective (i : D.J) : Function.Injective (𝖣.ι i) := by
   rcases (D.ι_eq_iff_rel _ _ _ _).mp h with (⟨⟨⟩⟩ | ⟨_, e₁, e₂⟩)
   · rfl
   · dsimp only at *
-    -- porting note: there were `cases e₁` and `cases e₂`, instead of the `rw`
+    -- Porting note: there were `cases e₁` and `cases e₂`, instead of the `rw`
     rw [← e₁, ← e₂]
     simp
 set_option linter.uppercaseLean3 false in
@@ -292,10 +292,10 @@ theorem preimage_image_eq_image' (i j : D.J) (U : Set (𝖣.U i)) :
     𝖣.ι j ⁻¹' (𝖣.ι i '' U) = (D.t i j ≫ D.f _ _) '' (D.f _ _ ⁻¹' U) := by
   convert D.preimage_image_eq_image i j U using 1
   rw [coe_comp, coe_comp]
-  -- porting note: `show` was not needed, since `rw [← Set.image_image]` worked.
+  -- Porting note: `show` was not needed, since `rw [← Set.image_image]` worked.
   show (fun x => ((forget TopCat).map _ ((forget TopCat).map _ x))) '' _ = _
   rw [← Set.image_image]
-  -- porting note: `congr 1` was here, instead of `congr_arg`, however, it did nothing.
+  -- Porting note: `congr 1` was here, instead of `congr_arg`, however, it did nothing.
   refine congr_arg ?_ ?_
   rw [← Set.eq_preimage_iff_image_eq, Set.preimage_preimage]
   change _ = (D.t i j ≫ D.t j i ≫ _) ⁻¹' _
@@ -305,7 +305,7 @@ theorem preimage_image_eq_image' (i j : D.J) (U : Set (𝖣.U i)) :
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.preimage_image_eq_image' TopCat.GlueData.preimage_image_eq_image'
 
--- porting note: the goal was simply `IsOpen (𝖣.ι i '' U)`.
+-- Porting note: the goal was simply `IsOpen (𝖣.ι i '' U)`.
 -- I had to manually add the explicit type ascription.
 theorem open_image_open (i : D.J) (U : Opens (𝖣.U i)) : IsOpen (𝖣.ι i '' (U : Set (D.U i))) := by
   rw [isOpen_iff]
@@ -347,7 +347,7 @@ structure MkCore where
   t_inter : ∀ ⦃i j⦄ (k) (x : V i j), ↑x ∈ V i k → (((↑) : (V j i) → (U j)) (t i j x)) ∈ V j k
   cocycle :
     ∀ (i j k) (x : V i j) (h : ↑x ∈ V i k),
-      -- porting note: the underscore in the next line was `↑(t i j x)`, but Lean type-mismatched
+      -- Porting note: the underscore in the next line was `↑(t i j x)`, but Lean type-mismatched
       (((↑) : (V k j) → (U k)) (t j k ⟨_, t_inter k x h⟩)) = ((↑) : (V k i) → (U k)) (t i k ⟨x, h⟩)
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.mk_core TopCat.GlueData.MkCore
@@ -446,7 +446,7 @@ def ofOpenSubsets : TopCat.GlueData.{u} :=
         continuity⟩
       V_id := fun i => by
         ext
-        -- porting note: no longer needed `cases U i`!
+        -- Porting note: no longer needed `cases U i`!
         simp
       t_id := fun i => by ext; rfl
       t_inter := fun i j k x hx => hx
@@ -476,7 +476,7 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
   intro x y e
   obtain ⟨i, ⟨x, hx⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective x
   obtain ⟨j, ⟨y, hy⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective y
-  -- porting note: now it is `erw`, it was `rw`
+  -- Porting note: now it is `erw`, it was `rw`
   -- see the porting note on `ι_fromOpenSubsetsGlue`
   erw [ι_fromOpenSubsetsGlue_apply, ι_fromOpenSubsetsGlue_apply] at e
   change x = y at e
@@ -504,7 +504,7 @@ theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) := by
     apply congr_arg
     exact Set.preimage_image_eq _ (fromOpenSubsetsGlue_injective U)
   · refine' ⟨Set.mem_image_of_mem _ hx, _⟩
-    -- porting note: another `rw ↦ erw`
+    -- Porting note: another `rw ↦ erw`
     -- See above.
     erw [ι_fromOpenSubsetsGlue_apply]
     exact Set.mem_range_self _
@@ -522,7 +522,7 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
   constructor
   · rintro ⟨x, rfl⟩
     obtain ⟨i, ⟨x, hx'⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective x
-    -- porting note: another `rw ↦ erw`
+    -- Porting note: another `rw ↦ erw`
     -- See above
     erw [ι_fromOpenSubsetsGlue_apply]
     exact Set.subset_iUnion _ i hx'

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

@@ -6,7 +6,6 @@ Authors: Andrew Yang
 import Mathlib.CategoryTheory.GlueData
 import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
 import Mathlib.Topology.Category.TopCat.Opens
-import Mathlib.Tactic.LibrarySearch
 
 #align_import topology.gluing from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 
@@ -135,7 +134,7 @@ theorem rel_equiv : Equivalence D.Rel :=
     rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩); exact id
     rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩); exact Or.inr ⟨x, e₁, e₂⟩
     let z := (pullbackIsoProdSubtype (D.f j i) (D.f j k)).inv ⟨⟨_, _⟩, e₂.trans e₃.symm⟩
-    have eq₁ : (D.t j i) ((pullback.fst : _ /-(D.f j k)-/ ⟶ D.V (j, i)) z) = x := by simp
+    have eq₁ : (D.t j i) ((pullback.fst : _ /-(D.f j k)-/ ⟶ D.V (j, i)) z) = x := by simp [z]
     have eq₂ : (pullback.snd : _ ⟶ D.V _) z = y := pullbackIsoProdSubtype_inv_snd_apply _ _ _
     clear_value z
     right

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

@@ -82,7 +82,7 @@ that the `U i`'s are open subspaces of the glued space.
 Most of the times it would be easier to use the constructor `TopCat.GlueData.mk'` where the
 conditions are stated in a less categorical way.
 -/
--- Porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 structure GlueData extends GlueData TopCat where
   f_open : ∀ i j, OpenEmbedding (f i j)
   f_mono := fun i j => (TopCat.mono_iff_injective _).mpr (f_open i j).toEmbedding.inj

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

@@ -426,7 +426,7 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
     convert congr_arg Subtype.val (h.t_inv k i ⟨x, hx'⟩) using 3
     refine Subtype.ext ?_
     exact h.cocycle i j k ⟨x, hx⟩ hx'
-  -- Porting note : was not necessary in mathlib3
+  -- Porting note: was not necessary in mathlib3
   f_mono i j := (TopCat.mono_iff_injective _).mpr fun x y h => Subtype.ext h
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.mk' TopCat.GlueData.mk'

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.

@@ -503,7 +503,7 @@ theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) := by
     erw [← ι_fromOpenSubsetsGlue, coe_comp, Set.preimage_comp]
     --  porting note: `congr 1` did nothing, so I replaced it with `apply congr_arg`
     apply congr_arg
-    refine' Set.preimage_image_eq _ (fromOpenSubsetsGlue_injective U)
+    exact Set.preimage_image_eq _ (fromOpenSubsetsGlue_injective U)
   · refine' ⟨Set.mem_image_of_mem _ hx, _⟩
     -- porting note: another `rw ↦ erw`
     -- See above.
@@ -529,7 +529,7 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
     exact Set.subset_iUnion _ i hx'
   · rintro ⟨_, ⟨i, rfl⟩, hx⟩
     rename_i x
-    refine' ⟨(ofOpenSubsets U).toGlueData.ι i ⟨x, hx⟩, ι_fromOpenSubsetsGlue_apply _ _ _⟩
+    exact ⟨(ofOpenSubsets U).toGlueData.ι i ⟨x, hx⟩, ι_fromOpenSubsetsGlue_apply _ _ _⟩
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.range_from_open_subsets_glue TopCat.GlueData.range_fromOpenSubsetsGlue
 

Classifies by adding issue number (#10745) to porting notes claiming was simp.

@@ -252,7 +252,7 @@ theorem image_inter (i j : D.J) :
   · rintro ⟨⟨x₁, eq₁⟩, ⟨x₂, eq₂⟩⟩
     obtain ⟨⟨⟩⟩ | ⟨y, e₁, -⟩ := (D.ι_eq_iff_rel _ _ _ _).mp (eq₁.trans eq₂.symm)
     · exact ⟨inv (D.f i i) x₁, by
-        -- Porting note: was `simp [eq₁]`
+        -- porting note (#10745): was `simp [eq₁]`
         -- See https://github.com/leanprover-community/mathlib4/issues/5026
         rw [TopCat.comp_app]
         erw [CategoryTheory.IsIso.inv_hom_id_apply]

Classifies by adding issue number (#10752) to porting notes claiming added dsimp only.

@@ -390,7 +390,7 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
   V i := (Opens.toTopCat _).obj (h.V i.1 i.2)
   f i j := (h.V i j).inclusion
   f_id i := by
-    -- Porting note: added `dsimp only`
+    -- Porting note (#10752): added `dsimp only`
     dsimp only
     exact (h.V_id i).symm ▸ IsIso.of_iso (Opens.inclusionTopIso (h.U i))
   f_open := fun i j : h.J => (h.V i j).openEmbedding

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

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

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
 import Mathlib.CategoryTheory.GlueData
-import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
 import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
 import Mathlib.Topology.Category.TopCat.Opens
 import Mathlib.Tactic.LibrarySearch

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

@@ -211,14 +211,14 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
     rw [← (InvImage.equivalence _ _ D.rel_equiv).eqvGen_iff]
     refine' EqvGen.mono _ (D.eqvGen_of_π_eq h : _)
     rintro _ _ ⟨x⟩
-    rw [←show (sigmaIsoSigma.{u, u} _).inv _ = x from
+    rw [← show (sigmaIsoSigma.{u, u} _).inv _ = x from
         ConcreteCategory.congr_hom (sigmaIsoSigma.{u, u} _).hom_inv_id x]
     generalize (sigmaIsoSigma.{u, u} D.V).hom x = x'
     obtain ⟨⟨i, j⟩, y⟩ := x'
     unfold InvImage MultispanIndex.fstSigmaMap MultispanIndex.sndSigmaMap
     simp only [Opens.inclusion_apply, TopCat.comp_app, sigmaIsoSigma_inv_apply,
       Cofan.mk_ι_app]
-    rw [←comp_apply, colimit.ι_desc, ←comp_apply, colimit.ι_desc]
+    rw [← comp_apply, colimit.ι_desc, ← comp_apply, colimit.ι_desc]
     erw [sigmaIsoSigma_hom_ι_apply, sigmaIsoSigma_hom_ι_apply]
     exact Or.inr ⟨y, ⟨rfl, rfl⟩⟩
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -208,7 +208,6 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
     rw [←
       show _ = Sigma.mk j y from ConcreteCategory.congr_hom (sigmaIsoSigma.{_, u} D.U).inv_hom_id _]
     change InvImage D.Rel (sigmaIsoSigma.{_, u} D.U).hom _ _
-    simp only [TopCat.sigmaIsoSigma_inv_apply]
     rw [← (InvImage.equivalence _ _ D.rel_equiv).eqvGen_iff]
     refine' EqvGen.mono _ (D.eqvGen_of_π_eq h : _)
     rintro _ _ ⟨x⟩

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -233,7 +233,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem ι_injective (i : D.J) : Function.Injective (𝖣.ι i) := by
   intro x y h
-  rcases(D.ι_eq_iff_rel _ _ _ _).mp h with (⟨⟨⟩⟩ | ⟨_, e₁, e₂⟩)
+  rcases (D.ι_eq_iff_rel _ _ _ _).mp h with (⟨⟨⟩⟩ | ⟨_, e₁, e₂⟩)
   · rfl
   · dsimp only at *
     -- porting note: there were `cases e₁` and `cases e₂`, instead of the `rw`

This reverts commit f3695eb2.

@@ -174,8 +174,10 @@ theorem eqvGen_of_π_eq
   let diagram := parallelPair 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap ⋙ forget _
   have : colimit.ι diagram one x = colimit.ι diagram one y := by
     dsimp only [coequalizer.π, ContinuousMap.toFun_eq_coe] at h
-    rw [← ι_preservesColimitsIso_hom, forget_map_eq_coe, types_comp_apply, h]
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [← ι_preservesColimitsIso_hom, forget_map_eq_coe, types_comp_apply, h]
     simp
+    rfl
   have :
     (colimit.ι diagram _ ≫ colim.map _ ≫ (colimit.isoColimitCocone _).hom) _ =
       (colimit.ι diagram _ ≫ colim.map _ ≫ (colimit.isoColimitCocone _).hom) _ :=
@@ -219,7 +221,7 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
       Cofan.mk_ι_app]
     rw [←comp_apply, colimit.ι_desc, ←comp_apply, colimit.ι_desc]
     erw [sigmaIsoSigma_hom_ι_apply, sigmaIsoSigma_hom_ι_apply]
-    exact Or.inr ⟨y, by dsimp [GlueData.diagram]; simp only [true_and]; rfl⟩
+    exact Or.inr ⟨y, ⟨rfl, rfl⟩⟩
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
     rfl
     dsimp only at *
@@ -410,8 +412,19 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
     simp only [Iso.inv_hom_id_assoc, Category.assoc, Category.id_comp]
     rw [← Iso.eq_inv_comp, Iso.inv_hom_id]
     ext1 ⟨⟨⟨x, hx⟩, ⟨x', hx'⟩⟩, rfl : x = x'⟩
-    rw [comp_app, ContinuousMap.coe_mk, comp_app, id_app, ContinuousMap.coe_mk, Subtype.mk_eq_mk,
-      Prod.mk.inj_iff, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
+    -- The next 9 tactics (up to `convert ...` were a single `rw` before leanprover/lean4#2644
+    -- rw [comp_app, ContinuousMap.coe_mk, comp_app, id_app, ContinuousMap.coe_mk, Subtype.mk_eq_mk,
+    --   Prod.mk.inj_iff, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
+    rw [comp_app] --, comp_app, id_app]
+    -- erw [ContinuousMap.coe_mk]
+    conv_lhs => erw [ContinuousMap.coe_mk]
+    erw [id_app]
+    rw [ContinuousMap.coe_mk]
+    erw [Subtype.mk_eq_mk]
+    rw [Prod.mk.inj_iff]
+    erw [Subtype.mk_eq_mk]
+    rw [Subtype.ext_iff]
+    rw [and_self_iff]
     convert congr_arg Subtype.val (h.t_inv k i ⟨x, hx'⟩) using 3
     refine Subtype.ext ?_
     exact h.cocycle i j k ⟨x, hx⟩ hx'

This reverts commit 26eb2b0a.

@@ -174,10 +174,8 @@ theorem eqvGen_of_π_eq
   let diagram := parallelPair 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap ⋙ forget _
   have : colimit.ι diagram one x = colimit.ι diagram one y := by
     dsimp only [coequalizer.π, ContinuousMap.toFun_eq_coe] at h
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [← ι_preservesColimitsIso_hom, forget_map_eq_coe, types_comp_apply, h]
+    rw [← ι_preservesColimitsIso_hom, forget_map_eq_coe, types_comp_apply, h]
     simp
-    rfl
   have :
     (colimit.ι diagram _ ≫ colim.map _ ≫ (colimit.isoColimitCocone _).hom) _ =
       (colimit.ι diagram _ ≫ colim.map _ ≫ (colimit.isoColimitCocone _).hom) _ :=
@@ -221,7 +219,7 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
       Cofan.mk_ι_app]
     rw [←comp_apply, colimit.ι_desc, ←comp_apply, colimit.ι_desc]
     erw [sigmaIsoSigma_hom_ι_apply, sigmaIsoSigma_hom_ι_apply]
-    exact Or.inr ⟨y, ⟨rfl, rfl⟩⟩
+    exact Or.inr ⟨y, by dsimp [GlueData.diagram]; simp only [true_and]; rfl⟩
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
     rfl
     dsimp only at *
@@ -412,19 +410,8 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
     simp only [Iso.inv_hom_id_assoc, Category.assoc, Category.id_comp]
     rw [← Iso.eq_inv_comp, Iso.inv_hom_id]
     ext1 ⟨⟨⟨x, hx⟩, ⟨x', hx'⟩⟩, rfl : x = x'⟩
-    -- The next 9 tactics (up to `convert ...` were a single `rw` before leanprover/lean4#2644
-    -- rw [comp_app, ContinuousMap.coe_mk, comp_app, id_app, ContinuousMap.coe_mk, Subtype.mk_eq_mk,
-    --   Prod.mk.inj_iff, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
-    rw [comp_app] --, comp_app, id_app]
-    -- erw [ContinuousMap.coe_mk]
-    conv_lhs => erw [ContinuousMap.coe_mk]
-    erw [id_app]
-    rw [ContinuousMap.coe_mk]
-    erw [Subtype.mk_eq_mk]
-    rw [Prod.mk.inj_iff]
-    erw [Subtype.mk_eq_mk]
-    rw [Subtype.ext_iff]
-    rw [and_self_iff]
+    rw [comp_app, ContinuousMap.coe_mk, comp_app, id_app, ContinuousMap.coe_mk, Subtype.mk_eq_mk,
+      Prod.mk.inj_iff, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
     convert congr_arg Subtype.val (h.t_inv k i ⟨x, hx'⟩) using 3
     refine Subtype.ext ?_
     exact h.cocycle i j k ⟨x, hx⟩ hx'

This includes all the changes from #7606.

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

@@ -174,8 +174,10 @@ theorem eqvGen_of_π_eq
   let diagram := parallelPair 𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap ⋙ forget _
   have : colimit.ι diagram one x = colimit.ι diagram one y := by
     dsimp only [coequalizer.π, ContinuousMap.toFun_eq_coe] at h
-    rw [← ι_preservesColimitsIso_hom, forget_map_eq_coe, types_comp_apply, h]
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [← ι_preservesColimitsIso_hom, forget_map_eq_coe, types_comp_apply, h]
     simp
+    rfl
   have :
     (colimit.ι diagram _ ≫ colim.map _ ≫ (colimit.isoColimitCocone _).hom) _ =
       (colimit.ι diagram _ ≫ colim.map _ ≫ (colimit.isoColimitCocone _).hom) _ :=
@@ -219,7 +221,7 @@ theorem ι_eq_iff_rel (i j : D.J) (x : D.U i) (y : D.U j) :
       Cofan.mk_ι_app]
     rw [←comp_apply, colimit.ι_desc, ←comp_apply, colimit.ι_desc]
     erw [sigmaIsoSigma_hom_ι_apply, sigmaIsoSigma_hom_ι_apply]
-    exact Or.inr ⟨y, by dsimp [GlueData.diagram]; simp only [true_and]; rfl⟩
+    exact Or.inr ⟨y, ⟨rfl, rfl⟩⟩
   · rintro (⟨⟨⟩⟩ | ⟨z, e₁, e₂⟩)
     rfl
     dsimp only at *
@@ -410,8 +412,19 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
     simp only [Iso.inv_hom_id_assoc, Category.assoc, Category.id_comp]
     rw [← Iso.eq_inv_comp, Iso.inv_hom_id]
     ext1 ⟨⟨⟨x, hx⟩, ⟨x', hx'⟩⟩, rfl : x = x'⟩
-    rw [comp_app, ContinuousMap.coe_mk, comp_app, id_app, ContinuousMap.coe_mk, Subtype.mk_eq_mk,
-      Prod.mk.inj_iff, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
+    -- The next 9 tactics (up to `convert ...` were a single `rw` before leanprover/lean4#2644
+    -- rw [comp_app, ContinuousMap.coe_mk, comp_app, id_app, ContinuousMap.coe_mk, Subtype.mk_eq_mk,
+    --   Prod.mk.inj_iff, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
+    rw [comp_app] --, comp_app, id_app]
+    -- erw [ContinuousMap.coe_mk]
+    conv_lhs => erw [ContinuousMap.coe_mk]
+    erw [id_app]
+    rw [ContinuousMap.coe_mk]
+    erw [Subtype.mk_eq_mk]
+    rw [Prod.mk.inj_iff]
+    erw [Subtype.mk_eq_mk]
+    rw [Subtype.ext_iff]
+    rw [and_self_iff]
     convert congr_arg Subtype.val (h.t_inv k i ⟨x, hx'⟩) using 3
     refine Subtype.ext ?_
     exact h.cocycle i j k ⟨x, hx⟩ hx'

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

@@ -168,7 +168,6 @@ theorem eqvGen_of_π_eq
         𝖣.diagram.fstSigmaMap 𝖣.diagram.sndSigmaMap)
       x y := by
   delta GlueData.π Multicoequalizer.sigmaπ at h
-  simp_rw [comp_app] at h
   -- Porting note: inlined `inferInstance` instead of leaving as a side goal.
   replace h := (TopCat.mono_iff_injective (Multicoequalizer.isoCoequalizer 𝖣.diagram).inv).mp
     inferInstance h

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

@@ -50,8 +50,6 @@ provided.
 * `TopCat.GlueData.ι_openEmbedding`: Each of the `ι i`s are open embeddings.
 
 -/
-set_option autoImplicit false
-
 
 noncomputable section
 

Changes the way the term is elaborated so that typeclass inference is tolerated and so that instances are allowed to come from the goal without re-inferring them.

@@ -356,8 +356,12 @@ structure MkCore where
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.mk_core TopCat.GlueData.MkCore
 
-theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x :=
-Subtype.eq <| by convert h.t_id j ▸ (h.cocycle j i j x <| h.V_id j ▸ ⟨⟩) using 1
+theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x := by
+  have := h.cocycle j i j x ?_
+  rw [h.t_id] at this
+  convert Subtype.eq this
+  rw [h.V_id]
+  trivial
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.mk_core.t_inv TopCat.GlueData.MkCore.t_inv
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module topology.gluing
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.GlueData
 import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
@@ -14,6 +9,8 @@ import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
 import Mathlib.Topology.Category.TopCat.Opens
 import Mathlib.Tactic.LibrarySearch
 
+#align_import topology.gluing from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
+
 /-!
 # Gluing Topological spaces
 

@@ -525,7 +525,7 @@ set_option linter.uppercaseLean3 false in
 #align Top.glue_data.range_from_open_subsets_glue TopCat.GlueData.range_fromOpenSubsetsGlue
 
 /-- The gluing of an open cover is homeomomorphic to the original space. -/
-def openCoverGlueHomeo (h : (⋃ i, (U i : Set α)) = Set.univ) :
+def openCoverGlueHomeo (h : ⋃ i, (U i : Set α) = Set.univ) :
     (ofOpenSubsets U).toGlueData.glued ≃ₜ α :=
   Homeomorph.homeomorphOfContinuousOpen
     (Equiv.ofBijective (fromOpenSubsetsGlue U)

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

@@ -141,20 +141,13 @@ theorem rel_equiv : Equivalence D.Rel :=
     rintro ⟨i, a⟩ ⟨j, b⟩ ⟨k, c⟩ (⟨⟨⟩⟩ | ⟨x, e₁, e₂⟩); exact id
     rintro (⟨⟨⟩⟩ | ⟨y, e₃, e₄⟩); exact Or.inr ⟨x, e₁, e₂⟩
     let z := (pullbackIsoProdSubtype (D.f j i) (D.f j k)).inv ⟨⟨_, _⟩, e₂.trans e₃.symm⟩
-    have eq₁ : (D.t j i) ((pullback.fst : _ /-(D.f j k)-/ ⟶ D.V (j, i)) z) = x := by
-      -- Porting note: was `simp`
-      -- See https://github.com/leanprover-community/mathlib4/issues/5026
-      rw [TopCat.pullbackIsoProdSubtype_inv_fst_apply, Subtype.coe_mk]
-      erw [CategoryTheory.GlueData.t_inv_apply]
+    have eq₁ : (D.t j i) ((pullback.fst : _ /-(D.f j k)-/ ⟶ D.V (j, i)) z) = x := by simp
     have eq₂ : (pullback.snd : _ ⟶ D.V _) z = y := pullbackIsoProdSubtype_inv_snd_apply _ _ _
     clear_value z
     right
     use (pullback.fst : _ ⟶ D.V (i, k)) (D.t' _ _ _ z)
     dsimp only at *
-    -- porting note: `rw + clear` was `substs e₁ e₃ e₄ eq₁ eq₂`
-    -- error: `failed to create binder due to failure when reverting variable dependencies`
-    rw [← e₁, ← e₃, ← e₄, ← eq₁, ← eq₂] at *
-    clear eq₂ eq₁ e₄ e₃ e₁
+    substs eq₁ eq₂ e₁ e₃ e₄
     have h₁ : D.t' j i k ≫ pullback.fst ≫ D.f i k = pullback.fst ≫ D.t j i ≫ D.f i j := by
       rw [← 𝖣.t_fac_assoc]; congr 1; exact pullback.condition
     have h₂ : D.t' j i k ≫ pullback.fst ≫ D.t i k ≫ D.f k i = pullback.snd ≫ D.t j k ≫ D.f k j := by
@@ -462,6 +455,8 @@ def fromOpenSubsetsGlue : (ofOpenSubsets U).toGlueData.glued ⟶ TopCat.of α :=
 set_option linter.uppercaseLean3 false in
 #align Top.glue_data.from_open_subsets_glue TopCat.GlueData.fromOpenSubsetsGlue
 
+-- Porting note: `elementwise` here produces a bad lemma,
+-- where too much has been simplified, despite the `nosimp`.
 @[simp, elementwise nosimp]
 theorem ι_fromOpenSubsetsGlue (i : J) :
     (ofOpenSubsets U).toGlueData.ι i ≫ fromOpenSubsetsGlue U = Opens.inclusion _ :=
@@ -474,7 +469,7 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
   obtain ⟨i, ⟨x, hx⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective x
   obtain ⟨j, ⟨y, hy⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective y
   -- porting note: now it is `erw`, it was `rw`
-  -- https://github.com/leanprover-community/mathlib4/issues/5164
+  -- see the porting note on `ι_fromOpenSubsetsGlue`
   erw [ι_fromOpenSubsetsGlue_apply, ι_fromOpenSubsetsGlue_apply] at e
   change x = y at e
   subst e
@@ -502,7 +497,7 @@ theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) := by
     refine' Set.preimage_image_eq _ (fromOpenSubsetsGlue_injective U)
   · refine' ⟨Set.mem_image_of_mem _ hx, _⟩
     -- porting note: another `rw ↦ erw`
-    -- https://github.com/leanprover-community/mathlib4/issues/5164
+    -- See above.
     erw [ι_fromOpenSubsetsGlue_apply]
     exact Set.mem_range_self _
 set_option linter.uppercaseLean3 false in
@@ -520,7 +515,7 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
   · rintro ⟨x, rfl⟩
     obtain ⟨i, ⟨x, hx'⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective x
     -- porting note: another `rw ↦ erw`
-    -- https://github.com/leanprover-community/mathlib4/issues/5164
+    -- See above
     erw [ι_fromOpenSubsetsGlue_apply]
     exact Set.subset_iUnion _ i hx'
   · rintro ⟨_, ⟨i, rfl⟩, hx⟩

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

@@ -474,6 +474,7 @@ theorem fromOpenSubsetsGlue_injective : Function.Injective (fromOpenSubsetsGlue
   obtain ⟨i, ⟨x, hx⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective x
   obtain ⟨j, ⟨y, hy⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective y
   -- porting note: now it is `erw`, it was `rw`
+  -- https://github.com/leanprover-community/mathlib4/issues/5164
   erw [ι_fromOpenSubsetsGlue_apply, ι_fromOpenSubsetsGlue_apply] at e
   change x = y at e
   subst e
@@ -501,6 +502,7 @@ theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) := by
     refine' Set.preimage_image_eq _ (fromOpenSubsetsGlue_injective U)
   · refine' ⟨Set.mem_image_of_mem _ hx, _⟩
     -- porting note: another `rw ↦ erw`
+    -- https://github.com/leanprover-community/mathlib4/issues/5164
     erw [ι_fromOpenSubsetsGlue_apply]
     exact Set.mem_range_self _
 set_option linter.uppercaseLean3 false in
@@ -518,6 +520,7 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
   · rintro ⟨x, rfl⟩
     obtain ⟨i, ⟨x, hx'⟩, rfl⟩ := (ofOpenSubsets U).ι_jointly_surjective x
     -- porting note: another `rw ↦ erw`
+    -- https://github.com/leanprover-community/mathlib4/issues/5164
     erw [ι_fromOpenSubsetsGlue_apply]
     exact Set.subset_iUnion _ i hx'
   · rintro ⟨_, ⟨i, rfl⟩, hx⟩

@@ -17,7 +17,8 @@ import Mathlib.Tactic.LibrarySearch
 /-!
 # Gluing Topological spaces
 
-Given a family of gluing data (see `category_theory/glue_data`), we can then glue them together.
+Given a family of gluing data (see `Mathlib/CategoryTheory/GlueData.lean`), we can then glue them
+together.
 
 The construction should be "sealed" and considered as a black box, while only using the API
 provided.
@@ -31,7 +32,7 @@ provided.
 * `CategoryTheory.GlueData.ι`: The immersion `ι i : U i ⟶ glued` for each `i : ι`.
 * `TopCat.GlueData.Rel`: A relation on `Σ i, D.U i` defined by `⟨i, x⟩ ~ ⟨j, y⟩` iff
     `⟨i, x⟩ = ⟨j, y⟩` or `t i j x = y`. See `TopCat.GlueData.ι_eq_iff_rel`.
-* `Top.glue_data.mk`: A constructor of `glue_data` whose conditions are stated in terms of
+* `TopCat.GlueData.mk`: A constructor of `GlueData` whose conditions are stated in terms of
   elements rather than subobjects and pullbacks.
 * `TopCat.GlueData.ofOpenSubsets`: Given a family of open sets, we may glue them into a new
   topological space. This new space embeds into the original space, and is homeomorphic to it if
@@ -47,8 +48,8 @@ provided.
 * `TopCat.GlueData.image_inter`: The intersection of the images of `U i` and `U j` in `glued` is
     `V i j`.
 * `TopCat.GlueData.preimage_range`: The preimage of the image of `U i` in `U j` is `V i j`.
-* `Top.glue_data.preimage_image_eq_preimage_f`: The preimage of the image of some `U ⊆ U i` is
-    given by the preimage along `f j i`.
+* `TopCat.GlueData.preimage_image_eq_image`: The preimage of the image of some `U ⊆ U i` is
+    given by XXX.
 * `TopCat.GlueData.ι_openEmbedding`: Each of the `ι i`s are open embeddings.
 
 -/
@@ -84,8 +85,8 @@ such that
 We can then glue the topological spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 
-Most of the times it would be easier to use the constructor `Top.glue_data.mk'` where the conditions
-are stated in a less categorical way.
+Most of the times it would be easier to use the constructor `TopCat.GlueData.mk'` where the
+conditions are stated in a less categorical way.
 -/
 -- Porting note: removed @[nolint has_nonempty_instance]
 structure GlueData extends GlueData TopCat where
@@ -373,7 +374,7 @@ set_option linter.uppercaseLean3 false in
 instance (h : MkCore.{u}) (i j : h.J) : IsIso (h.t i j) := by
   use h.t j i; constructor <;> ext1; exacts [h.t_inv _ _ _, h.t_inv _ _ _]
 
-/-- (Implementation) the restricted transition map to be fed into `glue_data`. -/
+/-- (Implementation) the restricted transition map to be fed into `TopCat.GlueData`. -/
 def MkCore.t' (h : MkCore.{u}) (i j k : h.J) :
     pullback (h.V i j).inclusion (h.V i k).inclusion ⟶
       pullback (h.V j k).inclusion (h.V j i).inclusion := by
@@ -453,8 +454,8 @@ set_option linter.uppercaseLean3 false in
 #align Top.glue_data.of_open_subsets TopCat.GlueData.ofOpenSubsets
 
 /-- The canonical map from the glue of a family of open subsets `α` into `α`.
-This map is an open embedding (`from_open_subsets_glue_open_embedding`),
-and its range is `⋃ i, (U i : Set α)` (`range_from_open_subsets_glue`).
+This map is an open embedding (`fromOpenSubsetsGlue_openEmbedding`),
+and its range is `⋃ i, (U i : Set α)` (`range_fromOpenSubsetsGlue`).
 -/
 def fromOpenSubsetsGlue : (ofOpenSubsets U).toGlueData.glued ⟶ TopCat.of α :=
   Multicoequalizer.desc _ _ (fun x => Opens.inclusion _) (by rintro ⟨i, j⟩; ext x; rfl)
@@ -523,7 +524,7 @@ theorem range_fromOpenSubsetsGlue : Set.range (fromOpenSubsetsGlue U) = ⋃ i, (
     rename_i x
     refine' ⟨(ofOpenSubsets U).toGlueData.ι i ⟨x, hx⟩, ι_fromOpenSubsetsGlue_apply _ _ _⟩
 set_option linter.uppercaseLean3 false in
-#align Top.glue_data.range_fromOpenSubsetsGlue TopCat.GlueData.range_fromOpenSubsetsGlue
+#align Top.glue_data.range_from_open_subsets_glue TopCat.GlueData.range_fromOpenSubsetsGlue
 
 /-- The gluing of an open cover is homeomomorphic to the original space. -/
 def openCoverGlueHomeo (h : (⋃ i, (U i : Set α)) = Set.univ) :

Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: adomani <adomani@gmail.com>